Question

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

Explanation:

Step1: Identify adjacent side & angle

We know $\angle T = 62^\circ$, adjacent side $TS = \sqrt{10}$, and $TU$ is the hypotenuse.

Step2: Use cosine ratio definition

Cosine of an angle is $\frac{\text{adjacent}}{\text{hypotenuse}}$.
$\cos(62^\circ) = \frac{TS}{TU}$

Step3: Rearrange to solve for TU

$TU = \frac{TS}{\cos(62^\circ)}$
Substitute values: $TU = \frac{\sqrt{10}}{\cos(62^\circ)}$

Step4: Calculate numerical value

First, $\sqrt{10} \approx 3.162$, $\cos(62^\circ) \approx 0.4695$
$TU \approx \frac{3.162}{0.4695} \approx 6.7$

Answer:

$6.7$