Question

find m∠u.
s t
3
4
u
write your answer as an integer or as a decimal rounded to the neares
m∠u = °
submit

Explanation:

Step1: Identify triangle type and trigonometric ratio

We have a right - triangle \( \triangle SUT \) with \( \angle S = 90^{\circ} \), \( ST = 3 \) (opposite to \( \angle U \)) and \( UT = 4 \) (hypotenuse). We can use the sine function, where \( \sin(\angle U)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{ST}{UT} \)

Step2: Calculate the sine of \( \angle U \)

Substitute the values: \( \sin(\angle U)=\frac{3}{4} = 0.75 \)

Step3: Find the measure of \( \angle U \)

To find \( \angle U \), we take the inverse sine (arcsin) of \( 0.75 \). So \( \angle U=\arcsin(0.75) \)
Using a calculator, \( \arcsin(0.75)\approx48.59^{\circ} \) (rounded to the nearest hundredth, and if we round to the nearest degree, it is \( 49^{\circ} \), but following the instruction of decimal rounded to the nearest, let's assume to the nearest tenth or hundredth. Let's calculate it precisely: \( \arcsin(3/4)\approx48.59037789^{\circ} \)

Answer:

\( 48.6^{\circ} \) (or \( 48.59^{\circ} \) or \( 49^{\circ} \) depending on the rounding requirement, but the most accurate decimal rounded to the nearest tenth is \( 48.6^{\circ} \))