Question

find uv.
u
v
56°
4
t
write your answer as an integer or as a
decimal rounded to the nearest tenth.
uv =
submit

Explanation:

Step1: Identify adjacent/hypotenuse for $\angle V$

In right triangle $UTV$, $\angle T =90^\circ$, $TV=4$, $\angle V=56^\circ$. $\cos(56^\circ)=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{TV}{UV}$

Step2: Rearrange to solve for $UV$

$UV=\frac{TV}{\cos(56^\circ)}=\frac{4}{\cos(56^\circ)}$

Step3: Calculate final value

$\cos(56^\circ)\approx0.5592$, so $UV\approx\frac{4}{0.5592}\approx7.2$

Answer:

$7.2$