Questions: Solve the right triangle. Find the length of the side opposite to the given angle. (Round your answer to two decimal places.) Find the length of the side adjacent to the given angle. (Round your answer to two decimal places.) 35.57 Find the other acute angle. 3π/8 rad

Solution Steps

We are given the hypotenuse (38.5) and an angle (π/8). We want to find the length of the side opposite the given angle. We can use the sine function for this:

sin(π/8) = opposite / hypotenuse

opposite = 38.5 * sin(π/8) opposite ≈ 38.5 * 0.3827 opposite ≈ 14.73

We are given the hypotenuse (38.5) and an angle (π/8). We want to find the length of the side adjacent to the given angle. We can use the cosine function:

cos(π/8) = adjacent / hypotenuse

adjacent = 38.5 * cos(π/8) adjacent ≈ 38.5 * 0.9239 adjacent ≈ 35.57

The sum of angles in a triangle is π radians. We are given one acute angle is π/8 and the other angle is a right angle, which is π/2 radians. Let the other acute angle be x.

x + π/8 + π/2 = π

x = π - π/2 - π/8

x = π - 4π/8 - π/8

x = 3π/8

Final Answer: