For the right triangles below, find the exact values of the side lengths h and b. If necessary, write your responses in simplified radical form. h=square b=4sqrt (2)

Step 1: Identify the triangles and their properties.We have two right triangles. The first triangle has a 30°-60°-90° angle, and the second triangle has a 45°-45°-90° angle. Step 2: Apply the properties of the triangles to find the unknown side lengths.For a 30°-60°-90° triangle, the ratio of the sides opposite the 30°, 60°, and 90° angles is 1:√3:2. In this case, the side opposite the 60° angle (the longer leg) is given as 8, so the hypotenuse (h) is twice the side opposite the 30° angle. For a 45°-45°-90° triangle, the ratio of the sides opposite the 45°, 45°, and 90° angles is 1:1:√2. In this case, the side opposite one of the 45° angles is given as 4, so the hypotenuse (b) is 4 times √2.Step 3: Calculate the values of h and b.For the first triangle, h = 2 * (8/√3) = 16/√3. To rationalize the denominator, multiply the numerator and denominator by √3 to get h = 16√3/3.For the second triangle, b = 4 * √2 = 4√2.So, the exact values of the side lengths h and b are:h = 16√3/3b = 4√2