Kirk vists Yellowstone Park and Old Faithful on a perfect day. His eyes are 6ft from the ground, and the geyser can reach heights ranging from 90 feet to 184 feet.

In the afternoon, Kirk returns and observes the geyser's spray reach a height of 123 feet when the angle of elevation is 37 degrees. How far from the geyser is Kirk standing to the nearest tenth of a foot?

The answer is suppose to be 155.3, could someone please help me? I COS, TAN, and SIN but I did not find the right answer.

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## Answers & Comments

## Verified answer

The triangle connects the top of the spray to Kirk's eyes to the point on the geyser directly in front of Kirk.

The height of the triangle is 123 (height of geyser) - 6 (height of Kirk's eyes) or 117 ft.

We have the angle of elevation and the side opposite of it and are looking for the adjacent side (how far Kirk is), so use tangent.

tan angle = opposite / adjacent

tan 37 = 117 / x

x = 117 / tan 37

x = 155.3 ft