Question

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.
3√4 inches
4√3 inches
8 inches
8√3 inches

1. choose the best answer.

apply the 30°-60°-90° triangle theorem. if the length of the shorter leg a of the triangle is 4 inches, what is the measure of the length of the longer leg b for the triangle to the nearest inch.
≈ 12 inches
4√2 inches
3√4 inches
≈ 7 inches

Explanation:

Question 7

Step1: Recall 30-60-90 Theorem

In a \(30^\circ - 60^\circ - 90^\circ\) triangle, the sides are in the ratio \(1 : \sqrt{3} : 2\), where the shorter leg (opposite \(30^\circ\)) is \(x\), the longer leg (opposite \(60^\circ\)) is \(x\sqrt{3}\), and the hypotenuse is \(2x\).

Step2: Identify \(x\) and calculate hypotenuse

Given the shorter leg \(x = 4\) inches. The hypotenuse is \(2x\). Substitute \(x = 4\): \(2\times4 = 8\) inches.

Step1: Recall 30-60-90 Theorem

In a \(30^\circ - 60^\circ - 90^\circ\) triangle, the longer leg (opposite \(60^\circ\)) is \(x\sqrt{3}\), where \(x\) is the shorter leg.

Step2: Identify \(x\) and calculate longer leg

Given \(x = 4\) inches. The longer leg \(b = x\sqrt{3}=4\sqrt{3}\). Calculate \(4\sqrt{3}\approx4\times1.732\approx6.928\approx7\) inches (to the nearest inch).

Answer:

8 inches (the option with "8 inches")

Question 8