SAT Right triangles and trigonometry Practice Question 12 (Medium)

Question bank / Right triangles and trigonometry

Math · Geometry and TrigonometryMedium

A surveyor stands $50$ meters from the base of a building on level ground and measures the angle of elevation to the top of the building as $40^\circ$ . To the nearest meter, what is the height of the building? (Ignore the surveyor's height.)

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Answer: 42

The height $h$ is opposite the $40^\circ$ angle, and the $50$ -meter distance is adjacent to it. So $\tan 40^\circ = \frac{h}{50}$ , and $h = 50\tan 40^\circ \approx 50(0.8391) \approx 41.96$ . To the nearest meter, the height is $42$ meters.

Using sine instead of tangent gives $50\sin 40^\circ \approx 32$ , which treats the $50$ -meter distance as the hypotenuse.

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