“Real-World” Trig Problems

You can draw your triangle either way: Angle of Depression = Angle of Elevation

Diagonal distance Height above ground Distance across

Ex 1) A roofer is working on your neighbor’s home today Ex 1) A roofer is working on your neighbor’s home today. If the roof is 25 ft. high, and the angle of elevation made by the roof is 61°. To the nearest foot, how long is the slant of the roof?

Ex 2) You are 55 ft from a tree Ex 2) You are 55 ft from a tree. The distance from your eyes to the top of the tree is 70 ft. Find the angle of elevation.

Problem A A library needs to build an access ramp for wheelchairs. The main entrance to the library is 8 ft above sidewalk level. If the architect designs the slope of the ramp in such a way that the angle of elevation is 5º, how long must the access ramp be? Round your answer to the nearest

Problem B A child is standing across the street from his apartment. His mother is on their balcony. The angle of depression from the mother’s eyes to the child’s eyes is 22°. If the distance between their eyes is 32 ft, how far is the child standing from his apartment building? Round to the nearest foot

Problem C The angle of depression from an eagle to a mouse on the ground is 35°. If the eagle is perched 40ft in the air, how far is the mouse from the eagle to the nearest tenth of a foot?

Problem D Quincy, who is flying in a hot air balloon, can see his car on the ground. If the straight line distance from Quincy to his car is 1000 ft, and the car is 800 ft away from the point directly below the hot air balloon, what is Quincy’s angle of depression?

Problem E A person is standing 40 ft from a flagpole and can see the top of the pole at a 35º angle of elevation. The person’s eye level is 4 ft from the ground. What is the height of the flagpole to the nearest foot

Problem F From the top of a 100ft tall building, a man observes a car moving toward the building. If the angle of elevation of the car changes from 22° to 46° during the period of observation, how far does the car travel?