Question

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

Explanation:

Step1: Identify adjacent side, angle

We know $\angle U = 51^\circ$, adjacent side $SU = \sqrt{30}$, and $TU$ is the hypotenuse.

Step2: Use cosine definition

Cosine of angle = adjacent/hypotenuse, so $\cos(51^\circ) = \frac{SU}{TU}$. Rearrange to solve for $TU$:
$TU = \frac{SU}{\cos(51^\circ)}$

Step3: Calculate values

First, $\sqrt{30} \approx 5.477$, $\cos(51^\circ) \approx 0.6293$. Substitute:
$TU \approx \frac{5.477}{0.6293} \approx 8.7$

Answer:

$8.7$