SAT Math Multiple Choice Question 697: Answer and Explanation

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Question: 697

7. Images

Alyssa determines that a floating balloon is 1,200 meters away from her at an angle of 42° from the ground, as in the figure above. What is the height, h, of the balloon from the ground? (sin 42° = 0.669, cos 42° = 0.743, tan 42° = 0.900)

  • A. 802.8 meters
  • B. 891.6 meters
  • C. 1,080 meters
  • D. 1,793 meters

Correct Answer: A

Explanation:

A

Advanced Mathematics (triangle trigonometry) EASY

Remember the definitions of the basic trigonometric functions: SOH CAH TOA. Since the "side of interest" (h) is the opposite side to the given angle (42°), and since we know the length of the hypotenuse (1,200), we should use SOH.

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Plug in the values:

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Substitute sin 42° = 0.669:

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Multiply by 1,002:

(1,200)(0.669) = 802.8 = h

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