Question

1. choose the best answer.

apply the 45°-45°-90° triangle theorem to find the length of the hypotenuse of a right triangle with the length of leg a 5 inches.
10 inches
25 inches
2√5 inches
5√2 inches

1. choose the best answer.

apply the 45°-45°-90° triangle theorem. if the length of the hypotenuse of the triangle is 7 cm, what is the measure of the length of side b to the nearest centimeter?
≈ 7 cm
7√2 cm
2√7 cm
≈ 5 cm

Explanation:

Question 4

Step1: Recall 45-45-90 Theorem

In a \(45^\circ - 45^\circ - 90^\circ\) triangle, hypotenuse \(= \text{leg} \times \sqrt{2}\).

Step2: Apply the theorem

Given leg \(a = 5\) inches. So hypotenuse \(= 5\times\sqrt{2}=5\sqrt{2}\) inches.

Step1: Recall 45-45-90 Theorem

In a \(45^\circ - 45^\circ - 90^\circ\) triangle, \(\text{leg}=\frac{\text{hypotenuse}}{\sqrt{2}}\).

Step2: Substitute hypotenuse value

Hypotenuse \(= 7\) cm. So leg \(b=\frac{7}{\sqrt{2}}=\frac{7\sqrt{2}}{2}\approx\frac{9.899}{2}\approx 5\) cm (after rationalizing and approximating).

Answer:

\(5\sqrt{2}\) inches (the option with \(5\sqrt{2}\) inches)

Question 5