Question

1. choose the best 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 10√2.
2√10 in
√2√10 in
√(10√2) in
10 in

1. choose the best answer.

apply the 30°-60°-90° triangle theorem to find the length of the hypotenuse of a triangle if the length of the shorter leg is 4 inches.
8√3 inches
4√3 inches
3√4 inches
8 inches

Explanation:

Question 6:

Step1: Recall 45-45-90 Theorem

In a \(45^\circ - 45^\circ - 90^\circ\) 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 \(h = 10\sqrt{2}\), substitute into \(h = l\sqrt{2}\):
\(10\sqrt{2}=l\sqrt{2}\). Divide both sides by \(\sqrt{2}\): \(l = 10\).

Step1: Recall 30-60-90 Theorem

In a \(30^\circ - 60^\circ - 90^\circ\) triangle, the shorter leg (\(s\)) is opposite \(30^\circ\), the hypotenuse (\(h\)) is \(2s\), and the longer leg is \(s\sqrt{3}\).

Step2: Solve for hypotenuse

Given shorter leg \(s = 4\) inches, hypotenuse \(h = 2s\). Substitute \(s = 4\): \(h = 2\times4 = 8\) inches.

Answer:

10 in (the fourth option)

Question 7: