If a roof has a slope of 24:12, what is its angle to the horizontal?

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Multiple Choice

If a roof has a slope of 24:12, what is its angle to the horizontal?

Explanation:
When you convert a roof slope to an angle, use the tangent relationship: tan(theta) = rise/run. A slope of 24:12 means rise is 24 for every 12 of run, so tan(theta) = 24/12 = 2. Therefore theta = arctan(2) ≈ 63.4 degrees. Among the options, the one that matches closest is about 63 degrees. A 60-degree angle would require tan theta ≈ 1.732, not 2, and 45 or 30 degrees correspond to much smaller tangents (1 and ~0.577).

When you convert a roof slope to an angle, use the tangent relationship: tan(theta) = rise/run. A slope of 24:12 means rise is 24 for every 12 of run, so tan(theta) = 24/12 = 2. Therefore theta = arctan(2) ≈ 63.4 degrees. Among the options, the one that matches closest is about 63 degrees. A 60-degree angle would require tan theta ≈ 1.732, not 2, and 45 or 30 degrees correspond to much smaller tangents (1 and ~0.577).

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