Question

In the triangle rst, rs = 15, st = 25, rt = 20, which is the largest angle?

1) Angle R
2) Angle S
3) Angle T
4) Cannot be determined

Answer 1

The largest angle in triangle rst is angle T.

Step-by-step explanation:

To determine the largest angle in triangle rst, we can use the Law of Cosines. According to the Law of Cosines, the square of one side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of those sides multiplied by the cosine of the angle between them.

In this case, we know that rs = 15, st = 25, and rt = 20. Let's denote the angle opposite to rs as angle R, the angle opposite to st as angle S, and the angle opposite to rt as angle T. We can apply the Law of Cosines to find the largest angle:

rt^2 = rs^2 + st^2 - 2 * rs * st * cos(T)

20^2 = 15^2 + 25^2 - 2 * 15 * 25 * cos(T)

When we solve this equation, we find that cos(T) is approximately -0.1411. Since cosine of an angle is negative, we can conclude that angle T is obtuse. Therefore, the largest angle in triangle rst is angle T.