Question

Which of the following are true statements about a 30-60-90 triangle?

Answer 1

Answer:

A and E

Step-by-step explanation:

Answer 2

Answer:

The correct options are A and E.

Step-by-step explanation:

Triangle 30-60-90 means its a right angles triangle having interior angles 30, 60 and 90.

Let the shorter side be x.

$\cos(60^{\circ})=\frac{AB}{AC}$

$\frac{1}{2}=\frac{x}{AC}$

$AC=2x$

It means hypotenuse is twice long as the shorter leg. Option E is correct.

$\sin(60^{\circ})=\frac{BC}{AC}$

$\frac{\sqrt{3}}{2}=\frac{BC}{2x}$

$\frac{\sqrt{3}}{2}\times 2x=BC$

$\sqrt{3}x=BC$

It means the longer leg is √3 times as long as the shorter leg. Option A is correct.

Shorter leg = x

Longer leg =x√3

Hypotenuse = 2x

Therefore options A and E are correct.