Answer:
The lighthouse is 424 feet away.
Step-by-step explanation:
There is no other way to do this but to use one of the 6 trigonometry functions.
Drawing
Draw a dotted horizontal line.
judge an angle that could be 23o. Let it slant downward from the left side of the dotted line.
Draw another horizontal line that represents sea level.
Join the left side of the dotted line to the last line you drew. The angle on your right is also 23o.
Function
You have 6 trig functions to choose from. You have the lighthouse height (180 feet) the angle on your right, and the length on the horizontal representing the distance from the lighthouse base to the boat.
You have an angle
You have an opposite side
You have a horizontal line (the adjacent side)
You want to use the tangent function.
Tan(23) = opposite / ad
Tan(23) = 180 / adjacent Multiply both sides by the adjacent
adjacent*Tan(23)= 180 Divide by Tan(23)
adjacent = 180/Tan(23)
adjacent = 180 / 0.42447
adjacent = 424 feet.
