Question

find tu.
write your answer as an integer or as a decimal rounded to the nearest tenth.
tu =
submit
work it out

Explanation:

Step1: Identify triangle type

It's a right - triangle \( \triangle TUV \) with \( \angle U = 90^{\circ} \), hypotenuse \( TV = 4 \), and \( \angle V=49^{\circ} \). We need to find \( TU \), which is the side opposite to \( \angle V \).

Step2: Use sine function

The sine of an angle in a right - triangle is defined as \( \sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}} \). Here, \( \theta = 49^{\circ} \), opposite side is \( TU \), and hypotenuse \( TV = 4 \). So, \( \sin(49^{\circ})=\frac{TU}{4} \).

Step3: Solve for TU

We can re - arrange the formula to get \( TU = 4\times\sin(49^{\circ}) \). Using a calculator, \( \sin(49^{\circ})\approx0.7547 \). Then \( TU = 4\times0.7547 = 3.0188\approx3.0 \) (rounded to the nearest tenth).

Answer:

\( 3.0 \)