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A boat sights the top of a 40- foot lighthouse at an angle of

Question

A boat sights the top of a $40$ - foot lighthouse at an angle of elevation of $25$ degrees. Calculate the distance of the boat from the lighthouse (the horizontal distance) to the nearest tenth of a foot.

16.9

feet

18.7

feet

44.1

feet

85.8

feet

94.6

feet

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James Discussed

A boat sights the top of a

40

- foot lighthouse at an angle of elevation of

25

degrees. Calculate the distance of the boat from the lighthouse (the horizontal distance) to the nearest tenth of a foot.

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

Given, a boat sights the top of a

40

foot light house at an angle of elevation

25

degree

Then the lighthouse (horizontal ) the angle of elevation

= 90 - 25 = 65

degree

So, in right angle

△ A BC

tan 6 5^{0} = \frac{BC}{40}

\Rightarrow BC = 40 tan 6 5^{0}

\Rightarrow BC = 40 \times 2.1445

\Rightarrow BC = 85.78

foot

Then horizontal distance of lighthouse to boat

= 85.78

foot.

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Question Text	A boat sights the top of a $40$ - foot lighthouse at an angle of elevation of $25$ degrees. Calculate the distance of the boat from the lighthouse (the horizontal distance) to the nearest tenth of a foot.
Answer Type	Text solution:1
Upvotes	150

A boat sights the top of a 40- foot lighthouse at an angle of elevation of 25 degrees. Calculate the distance of the boat from the lighthouse (the horizontal distance) to the nearest tenth of a foot.

Text solutionVerified

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A boat sights the top of a $40$ - foot lighthouse at an angle of elevation of $25$ degrees. Calculate the distance of the boat from the lighthouse (the horizontal distance) to the nearest tenth of a foot.