Free Printable Right Triangle

1.

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

a)

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

b)

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

c)

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

d)

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

2.

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

a)

$27.7\degree$

b)

$31.7\degree$

c)

$58.3\degree$

d)

$62.3\degree$

3.

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)

33.6°

b)

39.8°

c)

50.2°

d)

56.4°

4.

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?

a)

16.7°

b)

17.5°

c)

72.5°

d)

73.3°

5.

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.

a)

14.3 in.

b)

20.5 in.

c)

21.3 in.

d)

22.6 in.

6.

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.

a)

3.0 in.

b)

9.8 in.

c)

10.5 in.

d)

12.8 in.

7.

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.

a)

183 meters

b)

250 meters

c)

366 meters

d)

683 meters

8.

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.

a)

14.2 feet

b)

17.1 feet

c)

47.6 feet

d)

55.2 feet

9.

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

a)

5/13

b)

5/12

c)

12/13

d)

13/12

10.

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

a)

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

b)

$\frac{1}{2}$

c)

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

d)

$\frac{2}{1}$

11.

For ΔABC, which one is equivalent to sin(A)?

a)

cos(B)

b)

sin(B)

c)

cos(C)

d)

tan(C)

12.

Given △ABC ~ △XYZ, what is the value of cos(Z)?

a)

5/13

b)

5/12

c)

12/13

d)

12/5

13.

The hypotenuse of a 45°-45°-90° triangle measures $7\sqrt{2}$ units.

What is the length of one leg of the triangle?

a)

7 unites

b)

$7\sqrt{2}$ units

c)

14 units

d)

$14\sqrt{2}$ units

14.

The hypotenuse of a 45°-45°-90° triangle measures $10\sqrt{5}$ in.
What is the length of one leg of the triangle?

a)

$5\sqrt{5}$

b)

$5\sqrt{10}$

c)

$10\sqrt{5}$

d)

$10\sqrt{10}$

15.

What are the angle measures of triangle ABC?

a)

m∠A = 30°, m∠B = 60°, m∠C = 90°

b)

m∠A = 90°, m∠B = 60°, m∠C = 30°

c)

m∠A = 60°, m∠B = 90°, m∠C = 30°

d)

m∠A = 90°, m∠B = 30°, m∠C = 60°

16.

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?

a)

60 ft.

b)

60\sqrt{3}

ft.

c)

120 ft.

d)

$120\sqrt{3}$ ft.

17.

Which set of numbers can represent the side lengths, in millimeters, of an obtuse triangle?

a)

8, 10, 14

b)

9, 12, 15

c)

10, 14, 17

d)

12, 15, 19

18.

Jamel is asked to create triangles using three of four given sticks. The sticks measure 3 in., 6 in., 7 in., and 8 in. He creates these 4 triangles.

Triangle 1: 3 in., 6 in., 7 in.

Triangle 2: 3 in., 6 in., 8 in.

Triangle 3: 3 in., 7 in., 8 in.

Triangle 4: 6 in., 7 in., 8 in.

a)

1

b)

2

c)

3

d)

4

19.

The lengths of two sides of a right triangle are 12 inches and 15 inches. What is the difference between the two possible lengths of the third side of the triangle? Round your answer to the nearest tenth.

a)

10.2 inches

b)

24.0 inches

c)

28.2 inches

d)

30.0 inches

20.

The longest side of an isosceles obtuse triangle measures 20 centimeters. The other two side lengths are congruent but unknown.

What is the greatest possible whole-number value of the congruent side lengths?

a)

9 cm

b)

10 cm

c)

14 cm

d)

15 cm

21.

A shelf is designed so it will fit in a 90º corner between two walls. The shelf has dimensions, rounded to the nearest tenth, as shown.

Will the shelf fit snugly in a 90º corner?

a)

$yes,\ 2\left(11^2\right)=\sqrt{242}^2$

b)

$no,\ \left(11+11\right)^2\ne\sqrt{242}^2$

c)

$no,\ 11^2+\sqrt{242}^2\ne11^2$

d)

$no,\ 11^2\ne\sqrt{242}^2$

22.

Giselle is building a small baseball infield for her brother. The infield should be in the shape of a square. Each side of the infield, between bases, measures 30 feet. The distance between home plate and second base, as shown in the picture, is 45 feet.

Which best describes the shape of the baseball field?

a)

$square,\ 30^2+30^2=45^2$

b)

$not\ square,\ \left(30+30\right)^2\ne45^2$

c)

$not\ square,\ 2\left(30\right)^2\ne45^2$

d)

$not\ square,\ \left(2\times30\right)^2\ne45^2$

23.

A company that makes mirrors sends their slightly flawed products to a discount store. This week, the company sent four mirrors to the discount store. Each mirror is approximately rectangular, with both lengths the same and both widths the same.

Based on these dimensions, which mirror is the closest to rectangular?

a)

1

b)

2

c)

3

d)

4

24.

Nadine is making a quilt. She can use a rectangle of any length and width, as long as the angles in the shape are right angles. Which pieces of fabric can Nadine use in the quilt? Check all that apply.

a)

1

b)

2

c)

4

d)

5

e)

6

25.

What is the length of the unknown leg in the right triangle?

a)

8 cm

b)

16 cm

c)

20 cm

d)

40 cm

26.

Which statements are true about the unknown side length in this right triangle? Check all that apply.

a)

The equation $a^2+\left(\sqrt{13}\right)^2=6^2$ can be used to find the unknown length.

b)

The equation $\left(\sqrt{13}\right)^2+b^2=6^2$ can be used to find the unknown length.

c)

The equation $\left(\sqrt{13}\right)^2+6^2=c^2$ can be used to find the unknown length.

d)

The length of the unknown leg is $\sqrt{23}$ meters.

e)

The length of the unknown leg is 7 meters.

27.

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.

a)

The total length of the Dogwood Trail is 16 kilometers.

b)

The total length of the Dogwood Trail is 24 kilometers.

c)

The Elm Trail is longer than the Dogwood Trail.

d)

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

e)

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

28.

Tamika builds a wooden skateboard ramp. The ramp measures 63 centimeters, and the length of its horizontal base is 60 centimeters, as shown.

In centimeters, what is the approximate height of the ramp? Round the answer to the nearest tenth of a centimeter.

(a)

29.

Carlos found that the length of the diagonal of his laptop monitor is $\sqrt{290}$
If the manufacturer rounds to the nearest whole inch, what size is the monitor as measured by the diagonal?

a)

12

b)

17

c)

97

d)

245

30.

Isaiah is jogging near his college. He runs south along Capitol Street for about 0.75 miles and east along H Street for about 1.2 miles. He then turns left and runs along Florida Avenue until he reaches his starting point. How long is his total run to the nearest hundredth of a mile?

a)

2.89 miles

b)

3.37 miles

c)

3.67 miles

d)

3.92 miles

31.

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.

a)

Mark will jog home a distance of 2.75 miles.

b)

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

c)

Mark will jog home a distance of 2.25 miles.

d)

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

e)

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

32.

What is the length of the hypotenuse in a right triangle with legs of length 14 and 48?

(a)

33.

Which is a perfect square?

a)

121

b)

140

c)

168

d)

195

34.

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?

a)

Holly is correct.

b)

Tamar is correct.

c)

Neither Holly nor Tamar is correct.

d)

Both Holly and Tamar are correct.

35.

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

a)

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.

b)

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.

c)

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.

d)

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.

36.

Denesh is creating a triangular flower bed using three pieces of wood. The two shorter pieces of wood have lengths of 7 feet and 24 feet. How long, in feet, should the third piece of wood be for Denesh to create a right triangle?

(a)

37.

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

a)

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

b)

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

c)

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

d)

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

38.

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

a)

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

b)

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

c)

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

d)

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

39.

Which set of numbers can represent the side lengths, in centimeters, of a right triangle?

a)

8, 12, 15

b)

10, 24, 26

c)

12, 20, 25

d)

15, 18, 20

40.

Which set of numbers can represent the side lengths, in inches, of an acute triangle?

a)

4, 5, 7

b)

5, 7, 8

c)

6, 7, 10

d)

7, 9, 12

41.

Two sides of an acute triangle measure 5 inches and 8 inches. The length of the longest side is unknown.

What is the greatest possible whole-number length of the unknown side?

a)

8 inches

b)

9 inches

c)

12 inches

d)

13 inches

Right Triangle

Total questions: 41

Worksheet time: 21mins

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