1) An airplane is flying 2 miles above ground level with a 15° angle of depression to a tree. It must fly 3 miles to be directly above the tree. 2) A fire department's longest ladder is 110 feet long and can be used up to 100 feet off the ground. The maximum angle of elevation for rescue is arctan(10/110) = 4.4°. 3) Given a 12 m flagpole with a 9 m shadow, the angle of elevation of the sun is arctan(9/12) = 41.8°.

1. UNIT 07 February
1. An airplane is flying at a height of 2 miles above the level ground. The angle of
depression from the plane to the foot of a tree is 15°. Find the distance that the
airplane must fly to be directly above the tree.
2. A fire department’s longest ladder is 110 feet long, and the safety regulation
states that they can use it for rescues up to 100 feet off the ground. What is the
maximun angle of elevation for the rescue ladder?
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.7.3.1

2. UNIT 07 February
3. A 12 m flagpole casts a 9 m shadow. Find the angle of elevation of the sun.
4. Find the height of the window of Maria if, when she looks out, she can see the
focus of a street lamp, which is 7 m away in a straight line, and the base of this is
looking down 45°.
5. Israel is going to throw a penalty in the soccer game where the goal is 2.44 m
tall. Strikes the ball with an angle of inclination of 38 °. If the penalty spot is 11
m, will he score goal?
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.7.3.2

3. UNIT 07 February
6. I am located at a point from which the angle of elevation to the top of a tower is
32°. If I approach 25 m to the base of the tower, the angle of elevation to the top
is 50°. What is the height of the tower?
7. A new homeowner has a triangular-shaped back yard. Two of the three sides
measure 53 ft and 42 ft and form an included angle of 135°. To determine the
amount of fertilizer and grass seed to be purchased, the owner has to know, or
at least approximate, the area of the yard. Find the area of the yard to the
nearest square foot.
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.7.3.3

4. UNIT 07 February
8. Two hikers see Mount Everest at an angle of 60 degrees. They approach it 3549
m, and now observe it with an angle of inclination of 80 °. Calculate the height of
Everest and the distance that the hikers are now.
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.7.3.4