Question

What is the value of θ for the acute angle in a right triangle? sin(θ)=cos(53°) Enter your answer in the box. θ= °

Answer 1

the value of θ for the acute angle in a right triangle, where sin(θ) = cos(53°), is 37 degrees.

Explanation:

In a right triangle, one of the angles is always 90 degrees, which is the right angle. The acute angle in a right triangle is the angle that is smaller than 90 degrees.

To find the value of θ for the acute angle in a right triangle, given that sin(θ) = cos(53°), we can use the trigonometric identity:

sin(θ) = cos(90° - θ)

Since sin(θ) = cos(53°), we can equate them:

cos(90° - θ) = cos(53°)

To find the acute angle θ, we solve for θ by equating the angles inside the cosine function:

90° - θ = 53°

Subtracting 53° from both sides:

90° - 53° = θ

θ= 37°

Therefore, the value of θ for the acute angle in a right triangle, where sin(θ) = cos(53°), is 37 degrees.