Question

Which of the following are true statements about a 30-60-90 triangle? Check all that apply.

Answer 1

Answer:

The longer leg is /3 times as long as the shorter leg.

The hypotenuse is twice as long as the shorter leg.

Step-by-step explanation:

Given triangle is 30- 60-90 degree triangle

WE use the common ratio of 30- 60-90 degree triangle

Common ratio is 1:1$\sqrt{3}$:2

     30      :      60     :       90

Short leg : long leg : hypotenuse

    x         :    $x\sqrt{3}$    : 2x

The hypotenuse is 2 times of the shorter leg

longer leg is square root (3) times the shorter leg

The longer leg is /3 times as long as the shorter leg.

The hypotenuse is twice as long as the shorter leg.

Answer 2

Answer:

C. The hypotenuse is twice as long as the shorter leg.  

B. The longer leg is √3 times as long as the shorter leg.

Step-by-step explanation:

A  30-60-90 triangle is a right triangle. Triangles with a right angle are called right triangles. A right triangle can only have a right angle. The representation of this problem is shown below. So let's demonstrate why the mentioned options are correct:

The hypotenuse of a right triangle is always opposite to the right angle. If we name $a$ as the shorter leg, for the sine of law is true that the hypotenuse is:

$\frac{H}{sin90}=\frac{a}{sin30} \\ \\ \frac{H}{1}=\frac{a}{0.5} \\ \\ \boxed{H=2a}$

So this fact tells us that the hypotenuse is twice as long as the shorter leg

The longer leg, let's name it $x$ can be calculated using Pythagorean Theorem:

$H^2=x^2+a^2 \\ \\ x=\sqrt{H^2-a^2} \\ \\ x=\sqrt{(2a)^2-a^2} \\ \\ x=\sqrt{4a^2-a^2} \\ \\ x=\sqrt{3a^2}=\sqrt{3}a$

So it is true that the longer leg is √3 times as long as the shorter leg.