Question

Identify the triangle that contains an acute angle for which the sine and cosine ratios are equal.

Triangle A B C has angle measures 50 degrees, 40 degrees, and 90 degrees.

Triangle A B C has angle measures 45 degrees, 45 degrees, 90 degrees. The lengths of sides A C and C B are congruent.

Triangle A B C has angle measures 68 degrees, 22 degrees, and 90 degrees.

Triangle A B C has angle measures 60 degrees, 30 degrees, and 90 degrees.

Answer 1

b

Explanation:

Answer 2

Explanation:

Given that, a series of triangle,

For the sine and cosine to be equal, then,

Sinθ = Cosθ

From, trigonometry identities

Sinθ = Cos(90-θ)

Then,

θ = 90-θ

θ + θ = 90

2θ = 90

θ = 90 / 2

θ = 45°

From the triangle given, using trigonometry ratio,

Sinθ = opposite / hypotenuse.

Sinθ = 20 / 25

Sinθ = 0.8

θ = arcsin(0.8)

θ = 53.13°

The other angles at the triangle is

90-53.13 = 36.87°.