High School

Set up a right triangle model for this problem and solve by using the reference table trigonometric ratio that applies.

A photographer stands 60 yards from the base of a lighthouse and observes that the angle between the ground and the top of the lighthouse is 41°. How tall is the lighthouse?

A. 45.3 yards
B. 52.2 yards
C. 39.4 yards

Answer :

Answer: B. 52.2 yards

Lighthouse is 52.2 yards tall.

Step-by-step explanation:

Let AB denotes the height of the lighthouse & BC denotes the distance between the base of a lighthouse and Photographer.

In Figure, ∠ACB = 41° & ∠ABC = 90°, Threrefore, Base is BC and perpendicular is AB.

As we know, tan(∠ACB) = [tex]\frac{Perpendicular}{Base}[/tex]

∴ tan 41° = [tex]\frac{AB}{BC}[/tex]

tan 41° = [tex]\frac{AB}{60}[/tex]

0.869286737 = [tex]\frac{AB}{60}[/tex]

AB = 52.2 yards ( approx.)

Thus, Height of the lighthouse is 52.2 yards


In reference to the angle of elevation (41 degrees), the adjacent side is 60 and the opposite side is the unknown.
Using tangent ratio:
tan 41 = opp/60
60 tan41 = opp
opp side = 52.2yards
LETTER B

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