From the top of a 108 foot lighthouse, the angle of depression of a boat at sea is 27º. find the horizontal distance from the boat to the base of the lighthouse, to the nearest foot. you must type all your steps of your solution. do not forget to round your final answer.

212 feet

Have a look at the image shown below. On that image, I've marked key details to focus on. Namely, the bottom right triangle has the angle CAB equal to 27 degrees because of the congruent alternate interior angles. This is the reference angle we'll base everything off of.

Opposite this angle is the side BC = 108 which is the lighthouse height. Adjacent to this angle is AB = x which is unknown. The goal is to solve for x

Use the tangent rule

tan(angle) = opposite/adjacent

tan(angle CAB) = CB/AB

tan(27) = 108/x <--- substitution

x*tan(27) = 108 <--- multiply both sides by x

x = 108/tan(27) <--- divide both sides by tan(27)

x = 211.96 <-- see note below

x = 212

note: use a calculator that has the trig functions sine, cosine, etc. You'll use the tan function for tangent. Make sure your calculator is in degree mode. the result you get is approximate as shown above, which will round to 212 when rounding to the nearest whole number.

answer: sorry i can't you.

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