Question

If the cos 36° = three fourths, then the sin 54° = _____. one half, because the angles are complementary 4 over 3, because the angles are supplementary three fourths, because the angles are complementary 1, because the angles are complementary

Answer 1

The value of sin 54° is √7/4.

Step-by-step explanation:

To find the value of sin 54°, we can use the fact that the angles 36° and 54° are complementary.

Since cos 36° is known to be three fourths, we can use the Pythagorean identity cos²θ + sin²θ = 1 to find sin 54°.

Solving for sin 54°, we have sin 54° = √(1 - cos² 54°).

Substituting cos² 54° = (3/4)², we get sin

54° = √(1 - (3/4)²)

= √(1 - 9/16)

= √(7/16)

= √7/4.

Therefore, the value of sin 54° is √7/4.