Question

in △rst, what is the length of segment rt? diagram: right triangle rst with right angle at s, rs = 26, ∠r = 45°, ∠t = 45°. options: 26√3, 62, 13, 26√2

Explanation:

Step1: Identify Triangle Type

△RST has a right angle at S and two 45° angles, so it's an isosceles right triangle (45-45-90 triangle). In such a triangle, the legs are equal, and the hypotenuse \( c \) is related to a leg \( a \) by \( c = a\sqrt{2} \).
Here, leg \( RS = 26 \), so leg \( ST = 26 \) (isosceles right triangle).

Step2: Calculate Hypotenuse RT

Using the 45-45-90 triangle formula, hypotenuse \( RT = RS \times \sqrt{2} \).
Substitute \( RS = 26 \): \( RT = 26\sqrt{2} \).

Answer:

\( 26\sqrt{2} \)