7
QuizMultiple Choice

Law of Sines — Quiz

Question 7 • Mathematics III

A support beam needs to be placed at a 28 degrees angle of elevation so that the top meets a vertical beam 1 point 6 meters above the horizontal floor. The vertical beam meets the floor at a 90 degrees angle. Law of sines: sine of cap A over A is equal to sine of cap b over b is equal to sine of cap c over c Approximately how far from the vertical beam should the lower end of the support beam be placed along the horizontal floor?

Answer
A
3 point 4 meters
B
4 point 4 meters
C
3 point 0 meters
D
3 point 9 meters

Explanation

The support beam, floor, and vertical beam form a right triangle. The 28° angle is at the floor, so the vertical height of 1.6 meters is opposite that angle and the floor distance is adjacent. Using tan(28°) = 1.6 ÷ distance gives distance = 1.6 ÷ tan(28°) ≈ 3.0 meters. Thus, the lower end should be placed about 3.0 meters from the vertical beam, choice C.

AI-written and checked against the verified answer.

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