A surveyor stands on one bank of a river. She sights a tree directly across the river, then walks 80 feet along her bank, perpendicular to her original line of sight. From this new position, the angle to the tree is 58°. To the nearest foot, how wide is the river? (tan 58° ≈ 1.600)
A50 feet
B128 feet
C68 feet
D42 feet
Explanation
The 80 feet she walked is adjacent to the 58° angle; the river width is opposite. Use tan: width = 80 × tan 58° = 80 × 1.600 = 128 ft. Choice A divides instead of multiplying (80 / 1.600 ≈ 50). C uses sin 58° × 80 ≈ 68 (wrong ratio). D uses cos 58° × 80 ≈ 42 (wrong ratio).
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