Question

apply the 45°-45°-90° triangle theorem to find the length of a leg of a right triangle if the length of the hypotenuse is 5√2 cm.
3 cm
5 cm
√2√5 cm
6 cm

1. choose the correct answer.

apply the 30°-60°-90° triangle theorem to find the length of the shorter leg of a triangle if the length of the hypotenuse is 20 cm.
3√20 cm
10 cm
17 cm
√(3√20) cm

Explanation:

First Question (45°-45°-90° Triangle)

Step1: Recall 45-45-90 Theorem

In a 45°-45°-90° triangle, the legs (\(l\)) are equal, and the hypotenuse (\(h\)) is \(l\sqrt{2}\), so \(h = l\sqrt{2}\).

Step2: Solve for leg length

Given \(h = 5\sqrt{2}\) cm, substitute into \(h = l\sqrt{2}\).
\(5\sqrt{2}=l\sqrt{2}\)
Divide both sides by \(\sqrt{2}\): \(l = 5\) cm.

Second Question (30°-60°-90° Triangle)

Step1: Recall 30-60-90 Theorem

In a 30°-60°-90° triangle, the shorter leg (\(s\)) is half the hypotenuse (\(h\)), so \(s=\frac{h}{2}\).

Step2: Calculate shorter leg

Given \(h = 20\) cm, substitute into \(s=\frac{h}{2}\).
\(s=\frac{20}{2}=10\) cm.

Answer:

First Question: B. 5 cm
Second Question: B. 10 cm