Josie is building a trapezoidal wall decoration out of wood. She wants to build two right triangles with a rectangular piece between them. To cut the wood, she needs to know the angles of the right triangles if she wants the slope of the diagonal sides to be 2. Using the inverse of tangent, what is the base angles of the triangles? Round your answer to the nearest whole degree.(1 point) °
To find the base angles of the right triangles, we need to use the inverse tangent function.
Given that the slope of the diagonal sides is 2, we can determine the angles as follows:
Let θ be the angle at the base of each right triangle.
The slope of the diagonal sides is equal to the tangent of the angle θ.
Therefore, tan(θ) = 2
Taking the inverse tangent of both sides, we get:
θ = arctan(2)
Using a calculator to find the arctan(2), we get:
θ ≈ 63.43 degrees
So, the base angles of each right triangle are approximately 63 degrees when rounded to the nearest whole degree.