Question

Why does sin54°≈0.809≈cos36° in a right triangle?

Answer 1

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Answer:

A

54° and 36° are complementary angles in the same right triangle. sin54° is the ratio of the opposite leg and the hypotenuse and cos36° is the ratio of the adjacent leg and the hypotenuse. In this triangle, the opposite leg of 54° and the adjacent leg of 36° are the same leg in the triangle.

Step-by-step explanation:

The answer explains itself.

The sum of angles in a triangle is 180°. When one of the angles is 90°, the sum of the other two angles is also 90°. That means those two acute angles are complementary (not supplementary).

The mnemonic SOH CAH TOA reminds you that ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse