Lesson 10 of 11

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9 min

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Keep the table beside you. Read each question twice: once for the angle, once for the sides.

Some Applications of Trigonometry — eight ideas and how they go
Idea	How it goes
Elevation	Height = walk × tan of the angle of elevation.
Depression	On level ground, depression from the top = elevation from the object.
Which ratio	Name the side you know and the side you want. That pair picks sin, cos or tan.
Two posts	Two readings, one tower: the two heights must match.
One vantage	Statue = whole column − pedestal.
One window	Tower = piece above + piece below.
Finding the angle	tan of the angle = height ÷ shadow.
The order	Read, draw, name, pick, divide, check.

A cell tower stands on flat ground. A 24 m walk reads 60° of elevation. How tall is it?

48 m
8√3 m
24√3 m

Where does the angle of depression open from?

The vertical wall of the cliff
The horizontal at the observer's eye, downward
The water line at the boat

The depression from a cliff top to a boat reads 45°. What does the elevation read at the boat?

45°
90°
It cannot be found

A sight line 24 m long reads 30° of elevation. Which ratio gives the height?

Cosine
Sine
Tangent

A far post reads 30°. A near post, 90 m closer, reads 60°. How far is the near post from the tower?

90 m
30 m
45 m

From 18 m, the pedestal reads 30°. The statue top reads 60°. How tall is the statue alone?

12√3 m
18√3 m
24√3 m

A window is 24 m from a tower. The top reads 45° up. The foot reads 45° down. How tall is the tower?

24√2 m
48 m
24 m

A 12 m pole casts a shadow 12 m long. What is the sun's angle?

45°
30°
60°

Chapter 9 is Some Applications of Trigonometry. Every problem in it asks you to name a right triangle. Next: Circles — lines that touch a circle at one point.

Reveal every answer to finish this lesson.

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