SAT Math Multiple Choice Question 994: Answer and Explanation

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Test Information

Question: 994


Triangle BUG shown is an isosceles right triangle. If the length of side UG is 5 units, what is the sine of ∠G?

  • A.
  • B.
  • C.
  • D. 1

Correct Answer: B



Difficulty: Medium

Category: Additional Topics in Math / Trigonometry

Strategic Advice: When a question doesn't appear to have enough information to answer it, look for clues in definitions of math terms.

Getting to the Answer: An isosceles right triangle is a right triangle that has two legs of equal length, making it a 45-45-90 triangle. This means ∠G is a 45° angle, and the sine of a 45° angle is, which is (B). You should consider memorizing the trig values for common angles (such as 30°, 45°, 60°, 90°, 180°, and 360°) to save yourself some time on Test Day. However, if you didn't recall the value of sin 45°, you could label the triangle using what you know about the side lengths of 45-45-90 triangles (that they are in the ratio or here,), and then use SOH CAH TOA to find that:

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