Trig Applications: Sides
With each problem, draw a diagram and completely label all necessary pieces. Establish a right triangle
trigonometric relationship and then solve each equation. Give exact answers for 30-60-90 triangles and
45-45-90 triangles. For other triangles, round the answer to 3 decimals.
1. A 15 foot ladder leans against a wall at an angle of elevation of 60o.
(a) How high up the wall does the ladder rest? Use 30-60-90 ratios to solve.
(b) How far from the wall is the base of the ladder? Use 30-60-90 ratios to solve.
(c) If the angle of elevation was changed to 45o, would the ladder reach higher up the wall or lower? Why?
(d) Find the height that the ladder would rest in part (c). Use 45-45-90 ratios to solve. Did this agree with your
conclusion?
2. A 50 foot pole has a support wire that runs from its top to the ground with an angle of depression of 75o.
(a) How far from the base of the pole does the wire connect to the ground?
(b) How much wire is used?
3. A flat 12 foot plank rests with one end on the ground and the other end upon a 4 foot ledge.
(a) How far from the base of the ledge is the far end of the plank?
(b) Write a trig ratio that could be used to find the angle of elevation of the plank.
(c) Write as many trig ratios as you can that could be used to find the angle of elevation.
Trig Applications: Sides
4. Jamie is 5’ 8” tall.
(a) Find the length of her shadow if the angle of elevation of the sun is 30.2o.
(b) At a different time of day, the angle of elevation of the sun is 64.7o. Find the length of her shadow now.
(c) Which time above do you think is the closest to noon? Why?
5. Some wire connects from a pole to a point on the ground at an angle of depression of 80o. On the ground,
the wire is 4.5 feet from the pole.
(a) How much wire is used?
(b) How high up the pole is the wire connected?
(c) If the same amount of wire is used, but the angle of depression is changed to 65o, then how far from base of
the pole does the wire touch the ground?
(d) Use the Pythagorean Theorem to find how high up the pole the wire is connected in part (c).
(e) Use a trig ratio to find how high up the pole the wire is connected in part (c).
(f) Are your answers in parts (d) and (e) the same?
Trig Applications: Sides
6. A large airplane flying at an altitude of 26,000 feet sights a smaller plane traveling at an altitude of 24,000
feet. The angle of depression between the two planes is 40o. What is the line of sight distance between the
two planes?
7. A building is 60 feet high. From a distance at point A on the ground, the angle of elevation to the top of the
building is 40o. From a little nearer at point B, the angle of elevation is 70o. Find the distance from point A
to point B. (hint: solve for z, then y, and then find x)
60
70
y
B
z
40
x
A
8. From a distance at point A on the ground, the angle of elevation to the top of the building is 60o. From a
little farther at point B, the angle of elevation is 45o. If point A is 50 feet from the building, how far is from
point B to the building? (hint: use 30-60-90 ratios to find y, then solve for x with 45-45-90 ratios)
60
50
45
B
A
x
9. From a window, I observe the top of a building across the 50 foot wide street at an angle of elevation of 74o.
I observe the base of the building at an angle of depression of 52o. Find the height of the building.
Trig Applications: Sides
10. When an angle of elevation is 54 degrees, a building casts a shadow that is 23 meters long. How tall is the
building?
11. A kite is flying at an angles of 42 degrees with the ground. All 70 meters of string has been let out. What is
the height of the kite?
12. Martha is 66 inches tall and her daughter Heidi is 33 inches tall. Who casts the longer shadow, Martha when
the sun is 80 degrees above the horizon or Heidi when the sun is 40 degrees above the horizon? By how
much?
13. A truck drives up a 30-meter incline at a 23 degree angle. How high (vertically) did the truck rise?
14. To find the distance from point A on the shore of a lake to point B on an island in the lake, surveyors locate
point P with mPAB  62 and mAPB  28 . If PA  350 m , what is AB?
15. 1. At a point on the ground 50 feet from the front of a tree, the angle of elevation to the top of the tree is 48.
Find the height of the tree.
16. A ladder is leaning against a wall. The foot of the ladder is 6.5 feet from the wall. The ladder makes an
angles of 74 with the level ground. How high on the wall does the ladder reach?
17. A wooden beam 24 feet long leans against a wall and makes and angle of 71 with the ground. How high up
the wall does the beam reach?
Trig Applications: Sides
18. A plane took off from a field and rose at an angle of 8 with the horizontal ground. As the plane flies over a
water tower, it has covered a distance from the take off point of 2000 feet. How far apart are the take off
point and the water tower?
19. A 20 foot ladder leans against a building and makes an angle of 72 with the ground. Find the distance
between the foot of the ladder and the building.
20. A boy visiting the Empire State Building from a point on the ground, A, which is 940 feet from the foot of
the building, C, The angle of elevation of the top, B, of the building as seen by the boy is 53. Find the
height of the building.
21. A straight road to the top of a hill is 2500 feet long and makes an angle of 12 with the horizontal. Find the
height of the hill.
22. A guywire attached to the top of a pole reaches a stake in the ground 20 feet from the foot of the pole and
makes an angle of 58 with the ground. How long is the guywire?
23. During its approach to Earth, the space shuttle’s glide angle changes. When the space shuttle is 6 miles from
the runway, its glide angle is about 21 degrees. What is the shuttle’s altitude at this point in its descent?
24. You are standing on one side of a river with a fried. Your friend looks directly across the river at a tree. You
stand 25 feet to the right of your friend and estimate the angle between your friend and the tree to be 79
degrees. Calculate the distance across the river from your friend to the tree. Suppose the actual angle is 74
degrees. How far off is your estimate?