Question

find $tu$.

write your answer as an integer or as a decimal rounded to the nearest tent
$tu = \square$
submit

Explanation:

Step1: Identify adjacent side to ∠U

Side $SU = \sqrt{30}$, adjacent to $51^\circ$

Step2: Relate to hypotenuse TU

Use cosine: $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$
$\cos(51^\circ) = \frac{\sqrt{30}}{TU}$

Step3: Solve for TU

Rearrange: $TU = \frac{\sqrt{30}}{\cos(51^\circ)}$
Calculate $\sqrt{30} \approx 5.477$, $\cos(51^\circ) \approx 0.6293$
$TU \approx \frac{5.477}{0.6293} \approx 8.7$

Answer:

8.7