Applications of Right Triangle Examples

Applications of Right Triangle Examples Date





1. Find the length of a guy wire that makes an angle of 4530 with the ground if the

wire is attached to the top of a tower 63.0 m high.









2. The angle of depression from a television tower to a point on the ground 36 m from

the bottom of the tower is 29.5 . Find the height of the tower.









3. Find the base angle of an isosceles triangle if the altitude is 4 ft and its base is 10 in.









4. Find the angle of depression of the sun’s rays when a 6’5” man casts a 7’ shadow.

5. At a point 200 ft from the base of a building, the angle of elevation to the bottom of a

smokestack is 35 , while the angle of elevation to the top is 53 . Find the height of

the smokestack alone.









6. While visiting the Sand Dunes National Park in Colorado, Ian approximated the angle

of elevation to the top of a sand dune to be 20 . After walking 800 ft closer, he

guessed that the angle of elevation had increased by 15 . Approximately how tall is

the dune he was observing?









7. A hot air balloon is between two spotters who are 2 mi apart. One spotter reports that

the angle of elevation of the balloon is 76 , and the other reports that it is 68. What

is the altitude of the balloon in feet?

8. A lost dog is 20 miles west and 8 miles south of his doghouse. If the dog wants to

travel directly to his home, what bearing should he take?









9. A man wandering in the desert walks 2.3 miles in the direction S 31W . He then

turns and travels another 18 miles in the direction of N 59W . At that time, how far is

he from his starting point, and what is his bearing from his starting point?









10. The Christmas Day Parade in Manhattan, New York started on 145th street. The

people walked north on this road for 4 miles, then turned on 34th street and walked for

3 more miles. If 34th street has a bearing of N 46E , then how far is the parade from

its starting point on 145th street and what bearing should be taken to get back?

Honors Trigonometry Name

WS: Applications of Rt. Triangles Date



1. From a hot-air balloon 2 km high, the angles of depression to two towns on either side

of the balloon are 81.2 and 13.5 . How far apart are the towns?









2. Inscription Rock rises almost straight upward from the valley floor. From one point

the angle of elevation of the top of the rock is 16.7 . From a point 168 m closer to the

rock, the angle of elevation of the top of the rock is 24.1 . How high is Inscription

Rock?









3. From the top of a 100 ft building a man observes a car moving toward him. If the

angle of depression of the car changes from 15 to 33 during the period of

observation, how far does the car travel?









4. For years the Woolworth skyscraper in New York held the record for the world’s

tallest office building. If the length of the shadow of the Woolworth building

increases by 17.4 m as the angle of elevation of the sun changes from 44 to 42 ,

then how tall is the building?