Question

find m∠t.
write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠t = °

Explanation:

Step1: Identify triangle type and sides

This is a right - triangle \( \triangle STU \) with \( \angle U = 90^{\circ} \), \( SU = 5.4 \) (adjacent to \( \angle T \)) and \( TU = 3.1 \) (opposite to \( \angle T \)). We can use the tangent function, where \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \). For \( \angle T \), \( \tan(\angle T)=\frac{SU}{TU} \) (since in \( \angle T \), the opposite side is \( SU \) and the adjacent side is \( TU \)).

Step2: Calculate \( \tan(\angle T) \)

Substitute the values of \( SU = 5.4 \) and \( TU = 3.1 \) into the tangent formula: \( \tan(\angle T)=\frac{5.4}{3.1}\approx1.7419 \)

Step3: Find \( \angle T \)

To find \( \angle T \), we take the arctangent (inverse tangent) of \( 1.7419 \). Using a calculator, \( \angle T=\arctan(1.7419) \). Calculating this, we get \( \angle T\approx59.9^{\circ} \) (rounded to the nearest tenth).

Answer:

\( 59.9 \)