Right Triangle Word Problems

A boat is 600 meters from the base of a cliff. Erika, who is sitting in the boat, notices that the angle of elevation to the top of the cliff is 32°. How high is the cliff?

(Round to the nearest tenth. Only the number, no units)

The height of a building is 250 feet. What is the angle of elevation from a point on the level ground 200 feet away from the building?

(Round to the nearest tenth. Only the number, no units)

Spencer is going snowboarding.  He rode the ski lift to the top of the mountain, which is at an altitude of 1500 feet.  The angle of elevation from the bottom to the top of the mountain is 25^o.  What is the length of the Spencer’s run (his trip down the hill)? 

• 3216.76 feet

• 633.93 feet

• 699.46 feet

• 3549.30 feet

A yacht is anchored 90 feet offshore from the base of a lighthouse.  The angle of elevation from the boat to the top of the lighthouse is 26 degrees.  The distance between the yacht and the top of the lighthouse is about 100 feet.  Which of these is closest to the height of the lighthouse? 

• 25 feet

• 45 feet 

• 110 feet 

• 135 feet 

A ramp is being built next to a 4-inch high sidewalk. The ramp's angle of inclination is 10 degrees. Estimate the horizontal length of the ramp to the nearest tenth of an inch.

The top of a ladder is leaning against a vertical wall, 12 feet above the floor. The bottom of the ladder is resting on the floor, 9 feet from the base of the wall. How long is the ladder?

• 15 feet

• 17 feet

• 19 feet

• 21 feet

Solve for the missing angle.

• 50

• 0.053

• 36.9

• 95

Susan is flying a kite, which gets caught in the top of a tree.  Use the diagram to estimate the height of the tree. 

• 63 ft

• 65 ft

• 74 ft

• 87 ft

Example 1: A boy who is flying a kite lets out 300 feet of string, which makes an angle of 52^o with the ground. Assuming that the string is stretched taut, find, to the nearest foot, how high the kite is above ground.

• 384 feet

• 236 feet

• 185 feet

• 45 feet

You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

• 25 feet

• 26 feet

• 27 feet

• 28 feet