Question

solve the right triangle.

write your answers in simplified, rationalized form. do not round.
rt =
m∠t =
m∠r =

Explanation:

Step1: Find hypotenuse \( RT \)

In right triangle \( RST \), legs \( RS = 9 \) and \( ST = 9 \). Use Pythagorean theorem: \( RT^2 = RS^2 + ST^2 \).
\( RT^2 = 9^2 + 9^2 = 81 + 81 = 162 \), so \( RT = \sqrt{162} = 9\sqrt{2} \).

Step2: Find \( m\angle T \)

Since \( RS = ST = 9 \), triangle is isosceles right triangle. In isosceles right triangle, acute angles are \( 45^\circ \). So \( m\angle T = 45^\circ \).

Step3: Find \( m\angle R \)

In right triangle, sum of angles is \( 180^\circ \). \( \angle S = 90^\circ \), \( \angle T = 45^\circ \), so \( m\angle R = 180^\circ - 90^\circ - 45^\circ = 45^\circ \).

Answer:

\( RT = 9\sqrt{2} \)
\( m\angle T = 45^\circ \)
\( m\angle R = 45^\circ \)