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In a right triangle, the length of the hypotenuse is 12 and the measure of one of the angles is 36. What is the length of the other leg

User Paul Kelly
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1 Answer

4 votes

Answer:

Either 9.71 (adjacent to 36°) or 7.05 (opposite 36°)

Explanation:

The question doesn't specify which leg is under question. Is it the adacent leg or the opposite leg? I'll assume adjacent.

We can use the acronym

SOHCAHTOA which is a helpful mnemonic for remembering the definitions of the trigonometric functions. For an angle other than the right angle, the following relationships are defined.

SOH: S is sine = Opposite/Hypotenuse

CAH: C is cosine = Adjacent/Hypotenuse

TOA: T is tangent = Opposite/Adjacent

For a side adjacent (A) to the 36° angle, we can use

Cosine = Adjacent/Hypotenuse

Since we know the hypotenuse (12) we can find A:

Cosine(36) = A/12

A = Cosine(36)*12

A = (0.809)*12

Adjacent = 9.71

====================

If the opposite leg is calculated, we would use

Sine= Opposite/Hypotenuse

Sine(36) = Opposite/12

O = (0.5877)*12

Opposite = 7.053

User Kenneth Salomon
by
5.1k points
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