SAT Math Multiple Choice Question 989: Answer and Explanation

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Question: 989

9.

In the right triangle above, cos x = 0.8. What is the value of cos y?

  • A.
  • B.
  • C.
  • D.

Correct Answer: B

Explanation:

B

Difficulty: Easy

Category: Additional Topics in Math / Trigonometry

Strategic Advice: Whenever trig values are given as decimal numbers, convert them to fractions so you can use the ratios given by SOH CAH TOA.

Getting to the Answer: The decimal 0.8 equals , which should make you think of a 3:4:5 triangle. Indeed, that's exactly what this triangle is. Draw a quick sketch and use SOH CAH TOA to place the side lengths in the correct places, ensuring that cos x = . That is, label the side adjacent to angle x as 4 and the hypotenuse 5. The remaining side must have length 3.

Again by SOH CAH TOA (and looking at angle y this time), cos y = , choice (B).

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