Question 34 Answer and Explanation _ACT January 2003 Form 59F Math Section

34. A surveyor took and recorded the measurements shown in the figure below. If the surveyor wants to use these 3 measurements to calculate the length of the pond, which of the following would be the most directly applicable?

F. The Pythagorean theorem

G. A formula for the area of a triangle

H. The ratios for the side lengths of 30°-60°-90° triangles

J. The ratios for the side lengths of 45°-45°-90° triangles

K. The law of cosines: For any △ABC, where a is the length of the side opposite ∠A, b is the length of the side opposite ∠B, and c is the length of the side opposite ∠C, a²= b²+ c²– 2bc cos(∠A)

Answer and Explanation

Your Answer is

Correct Answer is K

Explanation

When the two sides and the included angle are known, the law of cosines should be used. Choose K.