Questions: Solve the right triangle. Write your answers as integers or as decimals rounded to the nearest tenth. SU = m angle T = m angle S =

Transcript text: Solve the right triangle. Write your answers as integers or as decimals rounded to the nearest tenth. \[ \begin{aligned} S U & =\square \\ m \angle T & =\square \\ m \angle S & =\square \end{aligned} \]

Solution

Solution Steps

Step 1: Find the length of SU using the Pythagorean theorem.

In the right triangle TUS, TU = 4, TS = 6, and we need to find SU. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In triangle TUS, TS is the hypotenuse, so:

TS² = TU² + SU² 6² = 4² + SU² 36 = 16 + SU² SU² = 36 - 16 SU² = 20 SU = √20 SU ≈ 4.5

Step 2: Find m∠T using trigonometric ratios.

We can use the tangent function to find m∠T.

tan(T) = opposite/adjacent = SU/TU = √20 / 4

m∠T = arctan(√20 / 4) m∠T ≈ 56.3°

Step 3: Find m∠S using trigonometric ratios.

We can use the tangent function to find m∠S.

tan(S) = opposite/adjacent = TU/SU = 4/√20

m∠S = arctan(4/√20) m∠S ≈ 33.7°