Question

A wire is 30 inches long is bent into a triangle with sides measuring g 6 inches 11 inches 13 inches find the measure of the largest angle

Answer 1

Answer:

Largest angle is 94.22°

Explanation:

The sides of the triangle are given as 6 inches, 11 inches, 13 inches.

Now, we can find the respective interior angles of the triangle using cosine rule.

Thus, for the angle opposite 6 inches, let's label it A. Thus;

6² = 11² + 13² - 2(11 × 13)cos A

36 = 121 + 169 - 286cosA

36 = 290 - 286cos A

290 - 36 = 286cosA

cosA = 254/286

A = cos^(-1)0.8881

A = 27.36°

Similarly;

11² = 6² + 13² - 2(6 × 13)cos B

121 = 36 + 169 - 156cosB

121 = 205 - 156cos B

205 - 121 = 156cosB

cosB = 84/156

B = cos^(-1)0.5385

B = 57.42°

Sum of angles in a triangle is 180°

Thus;

C = 180 - (27.36 + 58.42)

C = 94.22°

Thus,largest angle is 94.22°