for the right triangles below, find the exact values of the side lengths b and h. if necessary, write your…

for the right triangles below, find the exact values of the side lengths b and h. if necessary, write your responses in simplified radical form.

for the right triangles below, find the exact values of the side lengths b and h. if necessary, write your responses in simplified radical form.

Answer

Explanation:

Step1: Solve for (b) using trigonometry in first triangle

In a 30 - 60 - 90 right - triangle, if the side opposite the 30° angle is (a), the side opposite the 60° angle is (a\sqrt{3}), and the hypotenuse is (2a). Here, the side opposite the 30° angle is 6. The side (b) is opposite the 60° angle. So, (b = 6\sqrt{3}).

Step2: Solve for (h) using trigonometry in second triangle

In a 45 - 45 - 90 right - triangle, the two legs are equal. If one leg is (x), the hypotenuse is (x\sqrt{2}). Here, one leg is 5, and (h) is the hypotenuse. So, (h = 5\sqrt{2}).

Answer:

(b = 6\sqrt{3}), (h = 5\sqrt{2})