Question

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

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( TUV \), we know angle \( V = 49^\circ \), hypotenuse \( UV = 4 \), and we need to find \( TU \), which is the side opposite angle \( V \). The sine ratio is defined as \( \sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}} \). So, \( \sin(49^\circ)=\frac{TU}{UV} \).

Step2: Substitute the known values

We know \( UV = 4 \) and \( \theta = 49^\circ \), so we can rewrite the equation as \( TU = UV\times\sin(49^\circ) \). Substituting \( UV = 4 \), we get \( TU = 4\times\sin(49^\circ) \).

Step3: Calculate the value

Using a calculator to find \( \sin(49^\circ) \approx 0.7547 \), then \( TU = 4\times0.7547 \approx 3.0188 \). Rounding to the nearest tenth, we get \( TU \approx 3.0 \).

Answer:

\( 3.0 \)