Geometry
Right Triangle Trig Applications
Name: __________________
Find the value of x. Round lengths of segments to the nearest tenth and angle measures to the nearest
degree.
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4.
2.
5.
3.
6.
Draw a picture for each situation and use right triangle trigonometry to solve:
7. A flagpole stands in the middle of a flat, level field. Fifty feet away from its base a surveyor measures the
angle to the top of the flagpole as 48°. How tall is the flagpole?
8. Liola walks 150 meters up a hill that has a grade of 3º. What horizontal distance has she covered?
9. A support cable for a 50 foot tower is to make a 60º angle with the ground. How long must the cable be? (The
cable goes to the top of the tower.)
10. Standing across the street 50 feet from a building, the angle to the top of the building is 40°. An antenna sits
on the front edge of the roof of the building. The angle to the top of the antenna is 52°. How tall is the
building?
11. How tall is the antenna in question 7? Find the total height using angle 52°. Then subtract away the height
of the building.
12. A very tall dude casts a shadow of 25 feet when the angle of the sun rays hits the ground at 20°. How tall is
the man?
13. I want to build a ramp for my dirt bike that runs over a little swamp in my back yard. I want the ramp to
incline at 37° and I know the swamp is 10 feet wide. How long does the ramp need to be.
14. A man is walking along a straight road. He notices the top of a tower rise away from him at an angle of 60 o
with the ground at the point where he is standing. If the height of the tower is h = 20 m, then what is the
distance (in meters) of the man from the tower?
15. A sunflower is blowing in the wind. The angle the flower makes with the ground is 75 o. If the stalk has
moved 2 inches horizontally, how long is the actual flower?
16. I want to tie up my boat to the dock. The boat is 10 feet away from the dock and the angle of the rope to the
dock will be 15 o. How long will my rope have to be?
17. A brick pathway is 30 yards long. A square courtyard is being built incorporating this pathway diagonally.
How long should each side of the square be? Note: the angle you will be using is 45°.
Create your own: You must write out a word problem similar to the ones I have provided. Be creative. Don’t
just find the heights of buildings, or use kites or balloons. Write out the problem and then solve it.
COSINE:
SINE:
TANGENT: