The hypotenuse of a 45°-45°-90° triangle measures 7 2 7\sqrt{2} 7 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> units. What is the length of one leg of the triangle?

7 2 7\sqrt{2} 7 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> units

14 2 14\sqrt{2} 1 4 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> units

The hypotenuse of a 45°-45°-90° triangle measures 10 5 10\sqrt{5} 1 0 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> in. What is the length of one leg of the triangle?

5 10 5\sqrt{10} 5 1 0 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

5 5 5\sqrt{5} 5 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

10 5 10\sqrt{5} 1 0 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

10 10 10\sqrt{10} 1 0 1 0 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

What are the angle measures of triangle ABC?

m ∠A = 90°, m ∠B = 60°, m ∠C = 30°

m ∠A = 30°, m ∠B = 60°, m ∠C = 90°

m ∠A = 60°, m ∠B = 90°, m ∠C = 30°

m ∠A = 90°, m ∠B = 30°, m ∠C = 60°

A garden is designed in the shape of a rhombus formed from 4 identical 30°-60°-90° triangles. The shorter distance across the middle of the garden measures 30 feet. What is the distance around the perimeter of the garden?

60 3 60\sqrt{3} 6 0 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> ft.

120 3 120\sqrt{3} 1 2 0 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> ft.

The diagram shows two different nature trails in a state park. The solid line shows the Dogwood Trail. The dashed line shows the Elm Trail. Which of the following statements are true about the lengths of the trails? Check all that apply.

The total length of the Dogwood Trail is 24 kilometers.

The difference between the lengths of the trails is 6 kilometers.

The total length of the Dogwood Trail is 16 kilometers.

The Elm Trail is longer than the Dogwood Trail.

The difference between the lengths of the trails is 2 kilometers.

Jesse and Mark are jogging along the route shown at a rate of 12 miles per hour. They start by jogging south along Capitol Street for 1 mile, then turn east on H Street and jog for 1.75 miles. At that point, Jesse is tired and decides to walk home along Florida Avenue at a rate of 5 miles per hour. Mark plans to jog back the way they came. Jesse wants to find out who will arrive home first and by how much time. Which statements should he consider when solving the problem? Check all that apply.

Mark will jog home a distance of 2.75 miles.

It will take Mark about 0.23 hours to jog home as found by 2.75 = 12(t).

Mark will get home about 0.17 hours (or 10 minutes) sooner.

Mark will jog home a distance of 2.25 miles.

Mark will get home about 0.21 hours (or 12.5 minutes) sooner.

Holly and Tamar completed the work in the table to determine if a triangle with side lengths of 40, 42, and 58 is a right triangle. Which best describes the accuracy of their solutions?

Neither Holly nor Tamar is correct.

Both Holly and Tamar are correct.

Which statement describes whether a right triangle can be formed using one side length from each of these squares?

Yes, a right triangle can be formed because the sum of the areas of the two smaller squares equals the area of the largest square.

Yes, a right triangle can be formed because the sum of the areas of the two smaller squares does not equal the area of the largest square.

No, a right triangle cannot be formed because the sum of the areas of the two smaller squares does not equal the area of the largest square.

No, a right triangle cannot be formed because the sum of the areas of the two smaller squares equals the area of the largest square.

Given right triangle XYZ, which correctly describes the locations of the sides in relation to ∠Y?

a is adjacent, b is opposite, c is the hypotenuse

a is opposite, b is adjacent, c is the hypotenuse

a is the hypotenuse, b is opposite, c is adjacent

a is adjacent, b is the hypotenuse, c is opposite

Given right triangle JKM, which correctly describes the locations of the sides in relation to ∠J?

a is the hypotenuse, b is adjacent, c is opposite

a is the hypotenuse, b is opposite, c is adjacent

a is adjacent, b is opposite, c is the hypotenuse

a is opposite, b is the hypotenuse, c is adjacent

Right Triangle Review

Authored by Maria Keenum

Mathematics

8th - 10th Grade

CCSS covered

Used 16+ times

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41 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which equation can be used to find the measure of angle LKJ?

$\cos^{-1}\left(\frac{8.9}{10.9}\right)=x$

$\cos^{-1}\left(\frac{10.9}{8.9}\right)=x$

$\sin^{-1}\left(\frac{8.9}{10.9}\right)=x$

$\sin^{-1}\left(\frac{10.9}{8.9}\right)=x$

Tags

CCSS.HSG.SRT.C.8

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which is the best approximation for the measure of angle ABC?

$27.7\degree$

$31.7\degree$

$58.3\degree$

$62.3\degree$

Tags

CCSS.HSG.SRT.C.8

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. The tree meets the ground at a right angle.

At approximately what angle does the wire meet the ground?

33.6°

39.8°

50.2°

56.4°

Tags

CCSS.HSG.SRT.C.8

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A theater production group is making frames to support wall-like props. Three-foot beams form right triangles with 10-foot beams to allow them to stand, as shown in the image.

What is x, the angle at which the diagonal beam meets the 10-foot beam at the top of the frame?

16.7°

17.5°

72.5°

73.3°

Tags

CCSS.HSG.SRT.C.8

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The equation $\cos\left(35\degree\right)=\frac{a}{25}$ can be used to find the length of $\overline{BC}$ .

What is the length of segment BC? Round to the nearest tenth.

14.3 in.

20.5 in.

21.3 in.

22.6 in.

Tags

CCSS.HSG.SRT.C.8

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The equation $\tan\left(55\degree\right)=\frac{15}{b}$ can be used to find the length of $\overline{AC}$ .

What is the length of $\overline{AC}$ ? Round to the nearest tenth.

3.0 in.

9.8 in.

10.5 in.

12.8 in.

Tags

CCSS.HSG.SRT.C.8

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Building A and building B are 500 meters apart. There is no road between them, so to drive from building A to building B, it is necessary to first drive to building C and then to building B.

About how much farther is it to drive than to walk directly from building A to building B? Round to the nearest whole number.

183 meters

250 meters

366 meters

683 meters

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Given right triangle QRS, what is the value of sin(30°)?

$\frac{\sqrt{3}}{3}$

$\frac{1}{2}$

$\frac{\sqrt{3}}{2}$

$\frac{2}{1}$

Tags

CCSS.HSG.SRT.C.6

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Right Triangle Review

Which equation can be used to find the measure of angle LKJ?

Which is the best approximation for the measure of angle ABC?

To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. The tree meets the ground at a right angle.

At approximately what angle does the wire meet the ground?

A theater production group is making frames to support wall-like props. Three-foot beams form right triangles with 10-foot beams to allow them to stand, as shown in the image.

What is x, the angle at which the diagonal beam meets the 10-foot beam at the top of the frame?

The equation $\cos\left(35\degree\right)=\frac{a}{25}$ can be used to find the length of $\overline{BC}$ .

What is the length of segment BC? Round to the nearest tenth.

The equation $\tan\left(55\degree\right)=\frac{15}{b}$ can be used to find the length of $\overline{AC}$ .

What is the length of $\overline{AC}$ ? Round to the nearest tenth.

Kari is flying a kite. She releases 50 feet of string. What is the approximate difference in the height of the kite when the string makes a 25 degree angle with the ground and when the string makes a 45 degree angle with the ground? Round to the nearest tenth.

Given right triangle RST, what is the value of sin(S)?

Given right triangle QRS, what is the value of sin(30°)?

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Right Triangle Review

Which equation can be used to find the measure of angle LKJ?

Which is the best approximation for the measure of angle ABC?

To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. The tree meets the ground at a right angle.At approximately what angle does the wire meet the ground?

A theater production group is making frames to support wall-like props. Three-foot beams form right triangles with 10-foot beams to allow them to stand, as shown in the image.What is x, the angle at which the diagonal beam meets the 10-foot beam at the top of the frame?

The equation cos⁡(35°)=a25\cos\left(35\degree\right)=\frac{a}{25}cos(35°)=25a​ can be used to find the length of BC‾\overline{BC}BC .What is the length of segment BC? Round to the nearest tenth.

The equation tan⁡(55°)=15b\tan\left(55\degree\right)=\frac{15}{b}tan(55°)=b15​ can be used to find the length of AC‾\overline{AC}AC .What is the length of AC‾\overline{AC}AC ? Round to the nearest tenth.

Kari is flying a kite. She releases 50 feet of string. What is the approximate difference in the height of the kite when the string makes a 25 degree angle with the ground and when the string makes a 45 degree angle with the ground? Round to the nearest tenth.

Given right triangle RST, what is the value of sin(S)?

Given right triangle QRS, what is the value of sin(30°)?

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. The tree meets the ground at a right angle.

At approximately what angle does the wire meet the ground?

A theater production group is making frames to support wall-like props. Three-foot beams form right triangles with 10-foot beams to allow them to stand, as shown in the image.

What is x, the angle at which the diagonal beam meets the 10-foot beam at the top of the frame?

The equation $\cos\left(35\degree\right)=\frac{a}{25}$ can be used to find the length of $\overline{BC}$ .

What is the length of segment BC? Round to the nearest tenth.

The equation $\tan\left(55\degree\right)=\frac{15}{b}$ can be used to find the length of $\overline{AC}$ .

What is the length of $\overline{AC}$ ? Round to the nearest tenth.