A 24-foot ladder leans against a wall, making a 65° angle with the level ground. To the nearest tenth of a foot, how high up the wall does the ladder reach? (sin 65° ≈ 0.906, cos 65° ≈ 0.423)
A10.1 feet
B21.7 feet
C26.5 feet
D56.7 feet
Explanation
The height up the wall is opposite the 65° angle, with the ladder as hypotenuse. Use sin: height = 24 × sin 65° = 24 × 0.906 ≈ 21.7 ft. Choice A uses cos (which gives the distance from the wall, not the height). C divides 24 by cos. D divides by sin.
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