10 1. Given right triangle ABC with hypotenuse AB=8.5 and mangle A=55^circ find AC and BC to the nearest hundredth.

To find the lengths of AC and BC in the right triangle ABC, we can use trigonometric ratios since we know one angle (other than the right angle) and the length of the hypotenuse.Step 1: Use the cosine function to find BC.The cosine of an angle in a right triangle is equal to the adjacent side divided by the hypotenuse. In this case, the cosine of angle A (55°) will give us the ratio of the length of BC (the adjacent side to angle A) to the length of AB (the hypotenuse). We know that AB = 8.5 and A = 55°, so we can plug these values into the equation: Now, solve for BC: Using a calculator, we find that: Step 2: Use the sine function to find AC.The sine of an angle in a right triangle is equal to the opposite side divided by the hypotenuse. In this case, the sine of angle A (55°) will give us the ratio of the length of AC (the opposite side to angle A) to the length of AB (the hypotenuse). We know that AB = 8.5 and A = 55°, so we can plug these values into the equation: Now, solve for AC: Using a calculator, we find that: Step 3: Round the results to the nearest hundredth.BC ≈ 4.88 (rounded to the nearest hundredth)AC ≈ 6.96 (rounded to the nearest hundredth)Answer:AC ≈ 6.96BC ≈ 4.88