Question

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

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 1

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

Answer 2

Answer: B. 52.2 yards

Lighthouse is 52.2 yards tall.

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) =
`(Perpendicular)/(Base)`

∴ tan 41° =
`(AB)/(BC)`

tan 41° =
`(AB)/(60)`

0.869286737 =
`(AB)/(60)`

AB = 52.2 yards ( approx.)

Thus, Height of the lighthouse is 52.2 yards