Question

ework: unit 3 - geometry question 44, 6.6.39 part 1 of 2 hw score: 91.39%, 53 of 58 points o points: 0 of 1 save on list sketch the right triangle and find the length of the side not given. (each length is in units.) leg = 35, hypotenuse = 91 sketch the right triangle. choose the correct answer below. o a o b. o c. o d. triangle diagrams on 34 on 35 on 36 on 37 on 38 on 39 on 40 on 41

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is hypotenuse, \(a,b\) are legs. Let one leg \(a = 35\), hypotenuse \(c = 91\), find the other leg \(b\). So \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(a = 35\), \(c = 91\) into the formula: \(b=\sqrt{91^{2}-35^{2}}\). Calculate \(91^{2}=8281\), \(35^{2}=1225\). Then \(91^{2}-35^{2}=8281 - 1225=7056\).

Step3: Take square root

\(b=\sqrt{7056}=84\).

For the sketch, in a right triangle, the hypotenuse is the longest side. So the triangle with one leg 35, hypotenuse 91, and the other leg 84 should have the right angle between the leg 35 and the leg 84, with hypotenuse 91 opposite the right angle. Looking at the options, option C (with leg 35, hypotenuse 91, and the other leg as the base) is correct.

Answer:

The length of the other leg is 84, and the correct sketch is option C.