Question

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?
2√7 cm
≈ 5 cm
7√2 cm
≈ 7 cm

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.
10 in
2√10 in
√2√10 in
√(10√2) in

Explanation:

Question 5

Step1: Recall 45-45-90 Triangle Theorem

In a \(45^\circ - 45^\circ - 90^\circ\) triangle, the legs are equal (\(a = b\)) and the hypotenuse \(c\) is related to the leg length \(a\) (or \(b\)) by the formula \(c=a\sqrt{2}\), so \(a = b=\frac{c}{\sqrt{2}}\).

Step2: Substitute hypotenuse value

Given \(c = 7\) cm, then \(b=\frac{7}{\sqrt{2}}\). Rationalize the denominator: \(b=\frac{7\sqrt{2}}{2}\approx\frac{7\times1.414}{2}\approx\frac{9.898}{2}\approx5\) cm.

Step1: Recall 45-45-90 Triangle Theorem

For a \(45^\circ - 45^\circ - 90^\circ\) triangle, \(c = a\sqrt{2}\) (where \(c\) is hypotenuse, \(a\) is leg). So, to find the leg \(a\) (or \(b\)) when \(c\) is known, we use \(a=\frac{c}{\sqrt{2}}\).

Step2: Substitute hypotenuse value

Given \(c = 10\sqrt{2}\), then \(a=\frac{10\sqrt{2}}{\sqrt{2}}\). The \(\sqrt{2}\) terms cancel out, so \(a = 10\) in.

Answer:

\(\approx 5\) cm (the option with \(\approx 5\) cm)

Question 6