Trigonometry Answer 5

Trigonometry Answer 5:

5. In the figure below, ÐY is a right angle and ÐX = 60°. If YZ is 5 units long, then how long is XY?

A. 5 units

B. 6 units

C. 15 units

D. 5Ö3 units

E. 30 units

The correct answer is D.

CXYZ is a 30° - 60° - 90° triangle.

Using the Pythagorean theorum, its sides are therefore in the ratio of 1: Ö3: 2

In other words, using relative measurements, the line segment opposite the 30° angle is 1 unit long, the line segment opposite the 60° angle is Ö3 units long, and the line segment opposite the right angle (the hypotenuse) is 2 units long.

In this problem, line segment XY is opposite the 30° angle, so it is 1 unit long.

Line segment YZ is opposite the 60° angle, so it is Ö3 units long.

Line segment XZ (the hypotenuse) if the angle opposite the right angle, so it is 2 units long.

So XY ÷ 5 = ¹/Ö3

XY ÷ 5 ´ 5= ¹/Ö3 ´ 5

XY = ⁵/Ö3

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