From the top of a lighthouse 240 feet high, the angle of depression to a boat out on the water is 23 degrees. Find the distance
1 answer:
Answer: 565 feet
This value is approximate.
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Explanation:
Imagine you are at the top of the lighthouse, and look straight horizontally outward. Then imagine looking down 23 degrees to spot the boat. This forms the angle of depression.
The adjacent angle complementary to this is 90-23 = 67 degrees. This is the interior angle of the triangle needed, and this angle is at the top of the triangle.
tan(angle) = opposite/adjacent
tan(67) = x/240
x = 240*tan(67)
x = 565.4045677977 approximately
x = 565 feet
The diagram is below.
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Answer:
y = 167°
Step-by-step explanation:
The vertex of the triangle = 154° ( alternate angle to 154° )
The triangle has 2 equal legs so is isosceles with 2 base angles congruent
base angle = =
= 13°
base angle and y are adjacent angles, lie on straight line AB and sum to 180°
y + 13° = 180° ( subtract 13° from both sides )
y = 167°