Question

Find the values of x and y. Write your answer in simplest form.

Answer 1

y = 6√3 and x = 6

Explanation:

this is a 30-60-90 triangle. The side opposite the 30° angle corresponds to the side of length 1 in the most basic 30-60-90 triangle; the side opp. 60° to the side of length √3; and the hyp. to the side of length 2.

To find y, write and solve an equation of ratios, as follows:

adj side adj side (adjacent to the 30° angle)

y √3

hypo hypo then (cross multiplying): 2y = 12√3, and

12 2 y = 6√3

If the hypo here is 12 and the adj side (y) is 6√3, then we can use the Pyth. Theorem to find the third side (x):

[12]² = [6√3]² - x² ↔ 144 = 36(3) - x² ↔ 36 = x². So x = 6 here.

Answer 2

x = 6

y ≈ 10. 40

Explanation:

Using the SOHCAHTOA principle we can solve for x and y since the angle is known and it is a right angle triangle.

hypotenuse = 12

adjacent = x

opposite = y

cos 60° = adjacent/hypotenus

cos 60° = x/12

cross multiply

x = 12 cos 60°

x = 12 × 0.5

x = 6

Finding y

sin 60° = opposite/hypotenuse

sin 60° = y/12

cross multiply

y = 12 sin 60°

y = 12 × 0.8660254038

y = 10.392304845

y ≈ 10. 40