College Entrance Exam Review

 $4^{-6}\cdot4^{-3}$  

•  $16^{-9}$  

•  $16^{18}$  

•  $4^{-9}$  

•  $4^{18}$  

 $5^3\cdot5^{-7}$  

•  $5^{-4}$  

•  $25^{-4}$  

•  $5^{-21}$  

•  $25^{-21}$  

The accompanying diagram shows a kite that has been secured to a stake in the ground with a 20-foot string. The kite is located 12 feet from the ground, directly over point X. What is the distance, in feet, between the stake and point X?

• 6

• 12

• 20

• 16

A 10-foot ladder is placed against the side of a building as shown in figure 1 below. The bottom of the ladder is 8 feet from the base of the building. In order to increase the reach of the ladder against the building, it is moved 4 feet closer to the base of the building as shown in figure 2.

To the nearest foot, how much further up the building does the ladder now reach? Show how you arrived at your answer.

• 3

• 9

• 6

• 4

A communications company is building a 30-foot antenna to carry cell phone transmissions. As shown in the diagram below, a 50-foot wire from the top of the antenna to the ground is used to stabilize the antenna.

Find, to the nearest degree, the measure of the angle that the wire makes with the ground.

• $30\degree$

• $37\degree$

• $50\degree$

• $137\degree$

An airplane took off at a constant angle of elevation. After the plane traveled for 25 miles, it reached an altitude of 5 miles, as modeled below.

To the nearest tenth of a degree, what was the angle of elevation?

• $12\degree$

• $11\degree$

• $11.5\degree$

• $10\degree$

In the diagram below of right triangle ABC,  $AC=8$  , and  $AB=17$  .



Which equation would determine the value of angle A? 

•  $\sin A=\frac{8}{17}$  

•  $\tan A=\frac{8}{15}$  

•  $\cos A=\frac{15}{17}$  

•  $\tan A=\frac{15}{8}$  

Yolanda is making a springboard to use for gymnastics. She has 8-inch-tall springs and wants to form a 16.5° angle with the base, as modeled in the diagram below.

To the nearest tenth of an inch, what will be the length of the springboard, x?

• $2.3$

• $8.3$

• $27.0$

• $28.2$

As shown in the diagram below, a building casts a 72-foot shadow on the ground when the angle of elevation of the Sun is 40°.

How tall is the building, to the nearest foot?

• $46$

• $60$

• $86$

• $94$

A man was parasailing above a lake at an angle of elevation of 32° from a boat, as modeled in the diagram below.

If 129.5 meters of cable connected the boat to the parasail, approximately how many meters above the lake was the man?

• $68.6$

• $80.9$

• $109.8$

• $244.4$