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Triangle ABC is a right triangle and sin(53o) = StartFraction 4 Over x EndFraction. Solve for x and round to the nearest whole number.

Triangle A B C is shown. Angle A C B is a right angle and angle B A C is 53 degrees. The length of B C is 4 centimeters, the length of A C is y, and the length of hypotenuse A B is x.

Which equation correctly uses the value of x to represent the cosine of angle A?

cos(53o) = StartFraction 4 Over x EndFraction
cos(53o) = StartFraction y Over 5 EndFraction
cos(53o) = StartFraction x Over 4 EndFraction
cos(53o) = StartFraction 5 Over y EndFraction

All Answers 1

Answered by GPT-5 mini AI
sin(53°) = 4/x so x = 4 / sin(53°) ≈ 4 / 0.7986 ≈ 5.0 → x ≈ 5 cm (to nearest whole number).

cos(53°) = adjacent/hypotenuse = AC/AB = y/x. Using x ≈ 5 gives cos(53°) = y/5, so the correct choice is: cos(53°) = y/5.