A ladder resting against a vertical wall makes a 60° elevation angle with its base standing 4.6 m away. What is the ladder's length:_________?
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Answer: D. 9.2 m
Explanation
Trigonometric ratios relate the lengths of right-angled triangle sides to the angles formed between them. The cosine of the sixty-degree elevation angle equals the adjacent base distance divided by the hypotenuse ladder length. Dividing the base distance of four point six by the cosine of sixty degrees, which is zero point five, yields nine point two meters. Right-triangle trigonometry uses sine, cosine, and tangent functions to solve for unknown side lengths and angles. The cosine function specifically represents the ratio of the adjacent side length to the hypotenuse length. The cosine of a sixty-degree angle is a standard trigonometric constant equal to exactly one half.
Option A results from multiplying instead of dividing by the cosine value, halving the actual length. Option B incorrectly assumes the ladder length equals the base distance without accounting for the angle. Option C represents an incorrect trigonometric calculation that fails to use the standard cosine ratio.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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