SAT Math Multiple Choice Question 194: Answer and Explanation

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Question: 194

14.

In the figure above, sin x° = . What is the perimeter of the figure?

  • A. 10 +
  • B. 7 +
  • C. 14 + 2
  • D. 39 + 2

Correct Answer: C

Explanation:

C SOHCAHTOA tells you that sine is , so if the side opposite the angle with measure x° is O and the hypotenuse is H, then . Solve for O, and you get . Now, you can use the Pythagorean theorem with the given side and substituting for O in order to solve for H: 102 + = H2. Solve the exponents, and then reduce the fraction: 100 + = H2; 100 + = H2. Subtract from both sides: 100 = . Divide both sides by , so 116 = H2. Square root both sides, and you find that H = 2.Using from above, you can solve for O: = 4. Add the sides and you get 14 + 2, which is (C).

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