Unit 5 Right Triangle Trig Review

Unit 5 Right Triangle Trig Review

Pythagorean Theorem

Multiple Choice

The legs of a right triangle measure 6 centimeters and 8 centimeters. How long is the hypotenuse in centimeters?

• 48 cm

• 14 cm

• 10 cm

• 7 cm

Multiple Choice

What is the value of x in the right triangle shown?

• 9

• 15

• 12

• 13

Multiple Choice

The area of a square is 49 square feet. Which of the following measures is closest to the length of its diagonal?

• 17.3 ft

• 24.5 ft

• 12.2 ft

• 9.9 ft

Trigonometric Ratios

Multiple Choice

What is the tangent of <E in the triangle?

• $\frac{g}{e}$

• $\frac{e}{f}$

• $\frac{e}{g}$

• $\frac{f}{e}$

Multiple Choice

What is the cosine of <X ? 

•  $\frac{\sqrt{11}}{13}$  

•  $\frac{7}{13}$  

•  $\frac{7\sqrt{11}}{13}$  

•  $\frac{13}{7}$  

Multiple Choice

In the figure, if $\sin x=\frac{8}{10}$  , what are  $\cos\ x\ and\ \tan\ x$  ? (Hint: Use Pythagorean Theorem to get the length of the other leg.)

• cos x = 6/10 and tan x = 8/6

• cos x = 2/10 and tan x = 8/2

• cos x = 4/10 and tan x = 4/2

• cos x = 9/10 and tan x = 8/9

Using Trig to find a Missing Side

Multiple Choice

What is the distance from the base of the ladder to the building? Round your answer to the nearest foot.

• 6 ft

• 19 ft

• 62 ft

• 10 ft

Multiple Choice

A ladder is leaning against the side of a building. The ladder is 20 feet long, and the angle between the ladder and the building is 10 degrees. About how far is the foot of the ladder from the building?

• 19.70 ft

• 3.53 ft

• 3.47 ft

• 18.72 ft

Multiple Choice

Angie looks up at an angle of 57 degrees and sees a hot air balloon 100 meters away. To the nearest meter, what is the value of x, the height of the hot air balloon above Angie's head?

• 54 m

• 84 m

• 154 m

• 119 m

Multiple Choice

An airplane makes a 15 degree angle of elevation from the runway when it takes off. The airplane pictured is 3,000 feet along the ground from its take-off point. At what height (h) is the airplane? Round the answer to the nearest foot.

• 902 ft

• 777 ft

• 2898 ft

• 804 ft

Multiple Choice

It is believed that the best angle to fly a kite is 30 degrees. If you fly a kite at this angle and let out 200 feet of string, approximately how high above the ground will the kite be?

• 100 ft

• 200 ft

• 150 ft

• 300 ft

Multiple Choice

KM is an altitude of triangle JKL, and KM is congruent to JM. The measure of angle LKM is 40 degrees, and ML = 9 cm. What is the approximate length of JK?

• 8.1 cm

• 15.1 cm

• 10.7 cm

• 13.7 cm

Multiple Choice

A bird flies from the top of a 30 ft. utility pole on a straight course to the top of a post 10 ft above the ground. If an angle of depression is 60 degrees, how far did the bird fly to reach the post? Round your answer to the nearest tenth.

• 23.1 ft

• 17.3 ft

• 34.6 ft

• 10.0 ft

Using Trig to find a Missing Angle

Multiple Choice

An object dropped from the top of the Leaning Tower of Pisa (181 ft) and lands 19 ft from the base.  

Which of these equations should be used to determine the angle (x) that the Leaning Tower of Pisa makes with the ground? 

•  $\tan\ x\ =\frac{181}{19}$  

•  $\cos\ x\ =\frac{181}{19}$  

•  $\tan\ x\ =\ \frac{19}{181}$  

•  $\cos\ x\ =\ \frac{19}{181}$  

Multiple Choice

A tourist views a deer from a height of 50 feet. The horizontal distance between the tourist and the deer is 135 feet. At what angle (x) should the tourist hold his camera to photograph the deer? Round your answer to the nearest degree.

• 70 degrees

• 50 degrees

• 60 degrees

• 40 degrees

Multiple Choice

Right triangle JKL is shown. What is the measure of <J ? Round your answer to the nearest degree.

• 22 degrees

• 19 degrees

• 68 degrees

• 72 degrees

Multiple Choice

The center pole of a tent is 9 ft long, and a side of the tent is 12 ft long. If a right angle is formed where the center pole meets the ground, what is the measure of Angle A to the nearest degree?

• 41 degrees

• 49 degrees

• 37 degrees

• 52 degrees

Multiple Choice

A lighthouse, which is 35 feet high, stands on a cliff that is 100 feet above sea level. The distance from the top of the lighthouse to a sailboat on the ocean is 400 feet.

What is the angle of elevation (x°) from the sailboat to the top of the lighthouse? Round the answer to the nearest degree.

• 71 degrees

• 18 degrees

• 20 degrees

• 56 degrees

Special Right Triangles

Multiple Choice

In the diagram shown of right triangle BAC, m<A = 90, m<B = 45, and AC = 7. What is the length of BC?

• 7

• $7\sqrt{2}$

• $14\sqrt{2}$

• $7\sqrt{3}$

Multiple Choice

What is the value of x, in inches?

• 10

• 5

• $5\sqrt{3}$

• $5\sqrt{2}$