Question

1. choose the correct answer. 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 $5\sqrt{2}$ cm. \bigcirc 5 cm \bigcirc 6 cm \bigcirc $\sqrt{2}\sqrt{5}$ cm \bigcirc 3 cm b. 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. \bigcirc $\sqrt{3}\sqrt{20}$ cm \bigcirc 10 cm \bigcirc $3\sqrt{20}$ cm \bigcirc 17 cm

Explanation:

Problem 7 (45-45-90 Triangle):

Step1: Recall 45-45-90 Theorem

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

Step2: Solve for leg \(a\)

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

Step1: Recall 30-60-90 Theorem

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

Step2: Solve for shorter leg \(a\)

Given \(c = 20\) cm, substitute into \(a=\frac{c}{2}\):
\(a=\frac{20}{2}=10\) cm.

Answer:

5 cm (corresponding to the option with "5 cm")

Problem B (30-60-90 Triangle):