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)

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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)

Answer 1

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√3/3 b = 4√2

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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)

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