Question

Jodi's Strategy: sin 5 degrees = 10/x

Kevin's Strategy: cos 85 degrees = 10/x
Both Jodi and Kevin's strategies will correctly solve for the length of the ramp. Explain why their solutions will be equal.

Answer 1

Jodi's strategy is based on the sine function, while Kevin's strategy is based on the cosine function. Both Jodi and Kevin are using trigonometric ratios to solve for the length of the ramp. Since sine and cosine are complementary functions, if sin(5 degrees) = cos(85 degrees), their solutions for x will be equal.

Step-by-step explanation:

Jodi's strategy is based on the sine function, while Kevin's strategy is based on the cosine function. Both Jodi and Kevin are using trigonometric ratios to solve for the length of the ramp. In this case, Jodi's equation is sin(5 degrees) = 10/x, and Kevin's equation is cos(85 degrees) = 10/x. Since sine and cosine are complementary functions, their values for a given angle will always add up to 90 degrees. Therefore, if sin(5 degrees) = cos(85 degrees), their solutions for x will be equal.