Question

In right triangle ABC, C is the right angle. What does sinB equal? options: sinB, cosB, cosA, not enough information

Answer 1

Answer: cos(A)

Explanation:

» From trigonometry,

`{ \tt{ \sin( \theta) = (opposite)/(hypotenuse) }} \\`

`{ \tt{ \red{ \sin(B) = (AC)/(AB) }}} \\`

» For cosine:

`{ \tt{ \cos( \theta) = (adjacent)/(hypotenuse) }} \\ \\ { \red{ \tt{ \cos(A) = (AC)/(AB) }}}`

» Therefore, sinB = cosA

Answer 2

Not enough information

explanation:

Taking sin here:

∠A + ∠B + ∠C = 180°

∠A + ∠B + 90 = 180°

∠A + ∠B = 90°

sin(A) + sin(B) = sin(90)

sin(B) = 1 - sin(A)

Taking cos here:

∠A + ∠B + ∠C = 180°

∠A + ∠B + 90 = 180°

∠A + ∠B = 90°

cos(A) + cos(B) = cos(90)

cos(A) + cos(B) = 0

cos(B) = -cos(A)