Question

solve the right triangle.
write your answers in simplified, rationalized form. do not round.
st =
su =
m∠t = 。

Explanation:

Step1: Find \(m\angle T\)

In a right - triangle, the sum of angles is \(180^{\circ}\). Since \(\angle U = 90^{\circ}\) and \(\angle S=45^{\circ}\), then \(m\angle T=180^{\circ}-90^{\circ}-45^{\circ}\)
\(m\angle T = 45^{\circ}\)

Step2: Find \(SU\)

Since \(\angle T=\angle S = 45^{\circ}\), the triangle \(TSU\) is an isosceles right - triangle (\(a = b\) in \(a^{2}+b^{2}=c^{2}\)). Here \(a = TU=2\sqrt{11}\), \(b = SU\). So \(SU=TU = 2\sqrt{11}\)

Step3: Find \(ST\)

Using the Pythagorean theorem \(c^{2}=a^{2}+b^{2}\), where \(a = TU = 2\sqrt{11}\), \(b = SU=2\sqrt{11}\) and \(c = ST\)
\(ST=\sqrt{(2\sqrt{11})^{2}+(2\sqrt{11})^{2}}=\sqrt{4\times11 + 4\times11}=\sqrt{44 + 44}=\sqrt{88}=2\sqrt{22}\)

Answer:

\(ST = 2\sqrt{22}\), \(SU = 2\sqrt{11}\), \(m\angle T=45^{\circ}\)