Before you read

Answer first — see what you already know.

A utility pole casts a 25-foot shadow when the sun is at a $55°$ angle of elevation. How tall is the pole? ( $tan 55° \approx 1.428$ )

A
17.5 ft
B
25 ft
C
35.7 ft
D
55 ft

Check your answer

Answer:

Before you read

Answer first — see what you already know.

Two office buildings are 100 m apart. From the rooftop of the shorter one (40 m tall), the angle of elevation to the top of the taller building is $30°$ . How tall is the taller building? ( $tan 30° \approx 0.577$ )

A
57.7 m
B
83.7 m
C
97.7 m
D
140 m

Check your answer

Answer:

Theory

Setting Up Trig Word Problems

Step 1: Draw a diagram and identify the right triangle.
Step 2: Label the known values and the unknown.
Step 3: Choose the right ratio (SOH-CAH-TOA) based on what you know and what you need.
Step 4: Solve.

Angle of elevation: Angle measured UP from horizontal.
Angle of depression: Angle measured DOWN from horizontal.

Angle of elevation problem

Key insight: The angle of elevation from point A to B equals the angle of depression from B to A (alternate interior angles).

Example 1

From the top of a 60 m lighthouse, the angle of depression to a boat is $20°$ . How far is the boat from the base? ( $\tan 20° \approx 0.364$ )

Angle of depression from top = angle of elevation from boat = $20°$

$\tan 20° = \frac{60}{d}$

$d = \frac{60}{0.364} \approx 164.8$ m

\approx

164.8 m

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