Question

In the triangle RST, RS = 15, ST = 25, RT = 20. Which is the largest angle? A. This cannot be determined B. ∠ RTS C. ∠ SRT D. ∠ RST

Answer 1

The largest angle is:

C. ∠ SRT

Step-by-step explanation:

In triangle RST, the largest angle is ∠ SRT. This can be determined by the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, RS + ST = 15 + 25 = 40 is greater than RT (20). Therefore, triangle RST is valid.

Additionally, the largest angle in a triangle is opposite the longest side. Since RT is the longest side, ∠ SRT is the largest angle in triangle RST. This conclusion is consistent with the fact that in a triangle, the largest angle corresponds to the longest side. Thus, ∠ SRT is the largest angle in triangle RST.

The Triangle Inequality Theorem plays a crucial role in determining the validity of a triangle and helps establish relationships between the sides and angles. In this specific triangle (RST), we use the theorem to confirm that the given side lengths (RS, ST, and RT) satisfy the conditions for forming a valid triangle. Once validity is established, identifying the largest angle becomes straightforward as it corresponds to the longest side, which, in this case, is RT. Therefore, ∠ SRT emerges as the largest angle in triangle RST.

Answer 2

So the answer is D. i.e. ∠RST.

The largest angle in triangle RST is ∠RST. Here's why:

Recall the largest angle - longest side relationship in triangles:

In any triangle, the angle opposite the longest side is the largest angle.

In this case, ST (25) is the longest side compared to RS (15) and RT (20).

Therefore, ∠RST, opposite the longest side ST, is the largest angle in triangle RST.