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1 month ago

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

Mathematics

2 answers:

Svet_ta [12.7K]1 month ago

8 0

Answer:

The longer leg measures √3 times the length of the shorter leg.

The hypotenuse is twice the length of the shorter leg.

Step-by-step explanation:

The triangle in question is a 30-60-90 degree triangle.

The conventional ratio in a 30-60-90 degree triangle is

1:1√3:2 $\sqrt{3}$ 30: 60: 90

Short leg: long leg: hypotenuse

: 2x

$x\sqrt{3}$ Therefore, the hypotenuse is twice that of the shorter leg, while the longer leg is √3 times the shorter leg.

The longer leg therefore measures √3 times longer than the shorter leg.

The hypotenuse is two times the length of the shorter leg.

Inessa [12.5K]1 month ago

3 0

Answer:

C. The hypotenuse measures twice the distance of the shorter leg.

B. The longer leg is √3 times the length of the shorter leg.

Step-by-step explanation:

A 30-60-90 triangle is considered a right triangle. Triangles containing a right angle are classified as right triangles. Only one right angle can exist in such a triangle. The representation of this case is illustrated below. Let’s clarify why the proposed statements are valid:

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

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

This indicates that the hypotenuse is double the length of the shorter leg

The longer leg, which we can call $x$ , can be determined with the Pythagorean Theorem:

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

Thus, it is accurate that the longer leg is √3 times longer than the shorter leg.

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