Question

One angle of a right triangle measures 60°. The side opposite this angle measures 15 inches.

Answer 1

Step-by-step explanation:

To solve this question I would use the sin rule.

The sin rule states that

$\frac{a}{ \sin(a) } = \frac{b}{ \sin(b) }$

Therefore if you substitute in your numbers you get:

$\frac{a}{ \sin(90) } = \frac{15}{ \sin(60) }$

If you rearrange that you get:

$a = \frac{15}{ \sin(60) } \times \sin(90)$

Therefore a = 17.3 Inches (to 3 sf)

This can also be done with basic trigonometry where you would get

$\sin(60) = \frac{15}{h}$

Rearranging to

$h = \frac{15}{ \sin(60) }$

meaning the answer is 13.7 inches

Answer 2

Answer:     10*sqrt(3)

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Work Shown:

h = unknown hypotenuse

sin(angle) = opposite/hypotenuse

sin(60) = 15/h

h*sin(60) = 15

h*sqrt(3)/2 = 15

h*sqrt(3) = 2*15

h*sqrt(3) = 30

h = 30/sqrt(3)

h = (30*sqrt(3))/(sqrt(3)*sqrt(3)

h = 30*sqrt(3)/3

h = (30/3)*sqrt(3)

h = 10*sqrt(3)