Question

In a right triangle, sin (4x + 3)° = cos (8x + 10)°. Solve for x. Round your answer

to the nearest hundredth if necessary.

Answer 1

To solve this problem, we will use the fact that sin (90 - θ) = cos θ for any angle θ. Therefore, we can rewrite the equation as:

sin (4x + 3)° = sin (90 - (8x + 10))°

Using the identity sin (90 - θ) = cos θ, we get:

sin (4x + 3)° = cos (8x + 10)°

sin (4x + 3)° = sin (80 - 8x)°

Now we have two cases to consider:

Case 1: 4x + 3 = 80 - 8x

Solving for x, we get:

12x = 77

x = 6.42

Case 2: 4x + 3 = 180 - (80 - 8x)

Solving for x, we get:

12x = 257

x = 21.42

Therefore, the solutions are x = 6.42 and x = 21.42.