Answer:
To draw a right triangle with a tangent ratio of 3/2 for one of the acute angles, we can choose any angle whose tangent is 3/2. Let's choose the angle θ.
We know that:
tangent ratio = opposite side / adjacent side
So, we can assign any value we want to the adjacent side, and then calculate the opposite side. Let's say the adjacent side is 2 units. Then, the opposite side would be:
opposite side = tangent ratio * adjacent side = (3/2) * 2 = 3
So, the sides of the triangle are:
adjacent side = 2
opposite side = 3
hypotenuse = √(2^2 + 3^2) = √13
We can now use trigonometry to find the measure of the other acute angle. The tangent of an angle is equal to the opposite side over the adjacent side, so we have:
tan(θ) = opposite side / adjacent side
tan(θ) = 3/2
Taking the inverse tangent of both sides, we get:
θ = tan^(-1)(3/2)
θ ≈ 56.3°
So, the other acute angle of the right triangle is approximately 56.3 degrees.