Question

Find the largest angle of △TUV. Assume that s is a positive number.

Answer 1

The largest angle of the triangle TUV is 83.59 degrees

Finding the largest angle of the triangle TUV

From the question, we have the following parameters that can be used in our computation:

The triangle TUV

Assuming that s is a positive number, we have the following equation

a² = b² + c² - 2bccos(A)

Where

A is the angle opposte the longest side

Using the above as a guide, we have the following:

39² = 37² + 20² - 2 * 37 * 30 * cos(A)

This gives

39² - (37² + 20²) = - 2 * 37 * 30 * cos(A)

-248 = -2220cos(A)

This gives

cos(A) = 0.1117

Evaluate

A = 83.59

Hence, the largest angle of the triangle TUV is 83.59 degrees

Answer 2

Remember that

In any triangle: The shortest side is always opposite the smallest interior angle. The longest side is always opposite the largest interior angle

so

In this problem

the largest interior angle is opposite to the longest side (TU)

that means

the largest interior angle is