Triangle ABC (not shown here) has a right angle at C. The length of side BC is 5.24 cm, and the length of side AC is 8.17 cm. Sketch the triangle and find ∠ABC, giving your answer correct to the nearest degree.

Step 1: Sketch the Triangle First, draw a right-angled triangle and label the corners as A, B, and C. Make sure that the right angle is at point C.

Step 2: Label the Sides Next, label the sides of the triangle. The side opposite the right angle (hypotenuse) is AC, which is 8.17 cm. The side adjacent to angle ABC is BC, which is 5.24 cm. The side opposite to angle ABC is AB, which we don't know the length of and don't need for this problem.

Step 3: Find ∠ABC We can find ∠ABC using the tangent of the angle, which is the ratio of the opposite side to the adjacent side. In this case, the tangent of ∠ABC is AB/BC. However, we don't know AB, but we do know that the sine of ∠ABC is BC/AC, so we can use that instead.

The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. So, sin(∠ABC) = BC/AC = 5.24 cm / 8.17 cm.

Step 4: Calculate ∠ABC To find the angle when you know the sine, you use the inverse sine function (also known as arcsine). So, ∠ABC = arcsin(5.24 cm / 8.17 cm).

Step 5: Round to the Nearest Degree Finally, calculate the value of ∠ABC and round it to the nearest degree. Make sure your calculator is set to give the answer in degrees, not radians.