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A surveyor is measuring the distance across a small lake. He has set up his transit on one side of the lake 90 feet from a piling that is directly across from a pier on the other side of the lake. From his transit, the angle between the piling and the pier is 40°. What is the distance between the piling and the pier to the nearest foot?

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Answer:

76 ft

Explanation:

[tex]\theta[/tex] = The angle between the piling and the pier = 40°

Distance between transit on one side of the lake and piling that is directly across = 90 ft

From the trigonometric identities we have

[tex]tan\theta=\dfrac{x}{90}\\\Rightarrow x=90tan\theta\\\Rightarrow x=90tan40\\\Rightarrow x=75.51896\ ft\approx 76\ ft[/tex]

The distance between the piling and the pier to the nearest foot is 76 ft

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