The captain of a boat knows that a lighthouse on the coast is 100 ft
away. if she measures the angle from the boat looking up to the top
of the light house to be 2º and she is 4 feet above the water when she
takes this measurement, how tall is the light house?

Height of the light house

Step-by-step explanation:

Distance of light house from boat = 100 ft

Angle of elevation from boat to the top of light house = 2°

Height above water while taking measurement = 4 ft

The figure of the situation is shown below.

For Δ ABC

Multiplying both sides by 100.

∴

Height of the light house

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)

c

step-by-step explanation: