Quiz about Right Triangle

Question 1

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 2

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

Accepted Answer

$$58.3\degree$$

Answer

$$27.7\degree$$

Answer

$$31.7\degree$$

Answer

$$62.3\degree$$

Question 3

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.

Accepted Answer

Answer

Answer

Answer

Question 4

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

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

Accepted Answer

Answer

Answer

Answer

Question 5

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.

Accepted Answer

183 meters

Answer

250 meters

Answer

366 meters

Answer

683 meters

Question 6

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.

Accepted Answer

Answer

Answer

Answer

Question 7

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

Accepted Answer

5/13

Answer

5/12

Answer

12/13

Answer

13/12

Question 8

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

Accepted Answer

8, 10, 14

Answer

9, 12, 15

Answer

10, 14, 17

Answer

12, 15, 19

Question 9

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.

Accepted Answer

3

Answer

1

Answer

2

Answer

4

Question 10

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.

Accepted Answer

10.2 inches

Answer

24.0 inches

Answer

28.2 inches

Answer

30.0 inches

Question 11

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?

Accepted Answer

14 cm

Answer

9 cm

Answer

10 cm

Answer

15 cm

Question 12

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?

Accepted Answer

$$not\ square,\ 2\left(30 ight)^2 e45^2$$

Answer

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

Answer

$$not\ square,\ \left(30+30 ight)^2 e45^2$$

Answer

$$not\ square,\ \left(2 imes30 ight)^2 e45^2$$

Question 13

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?

Accepted Answer

4

Answer

1

Answer

2

Answer

3

Question 14

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.

Accepted Answer

1

Accepted Answer

2

Accepted Answer

6

Answer

4

Answer

5

Question 15

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

Accepted Answer

20 cm

Answer

8 cm

Answer

16 cm

Answer

40 cm

Question 16

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

Accepted Answer

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

Accepted Answer

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

Accepted Answer

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

Answer

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

Answer

The length of the unknown leg is 7 meters.

Question 17

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.

Accepted Answer

The total length of the Dogwood Trail is 24 kilometers.

Accepted Answer

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

Answer

The total length of the Dogwood Trail is 16 kilometers.

Answer

The Elm Trail is longer than the Dogwood Trail.

Answer

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

Question 18

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?

Accepted Answer

Answer

Answer

Answer

Question 19

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?

Accepted Answer

3.37 miles

Answer

2.89 miles

Answer

3.67 miles

Answer

3.92 miles

Question 20

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.

Accepted Answer

Mark will jog home a distance of 2.75 miles.

Accepted Answer

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

Accepted Answer

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

Answer

Mark will jog home a distance of 2.25 miles.

Answer

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

Question 21

Which is a perfect square?

Accepted Answer

121

Answer

140

Answer

168

Answer

195

Question 22

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?

Accepted Answer

Tamar is correct.

Answer

Holly is correct.

Answer

Neither Holly nor Tamar is correct.

Answer

Both Holly and Tamar are correct.

Question 23

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

Accepted Answer

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.

Answer

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.

Answer

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.

Answer

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.

Question 24

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

Accepted Answer

10, 24, 26

Answer

8, 12, 15

Answer

12, 20, 25

Answer

15, 18, 20

Question 25

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

Accepted Answer

5, 7, 8

Answer

4, 5, 7

Answer

6, 7, 10

Answer

7, 9, 12

Question 26

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?

Accepted Answer

9 inches

Answer

8 inches

Answer

12 inches

Answer

13 inches

Right Triangle

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