Question

In ΔSTU, the measure of ∠U=90°, the measure of ∠T=47°, and ST = 7.2 feet. Find the length of US to the nearest tenth of a foot.​

Answer 1

Answer:

$US=5.3\ ft$

Step-by-step explanation:

we know that

In the right triangle STU

The sine of angle T is equal to the opposite side angle T divided by the hypotenuse

$sin(T)=\frac{US}{ST}$

substitute the values

$sin(47\°)=\frac{US}{7.2}$

$US=(7.2)sin(47\°)=5.3\ ft$

Answer 2

Answer:

The approximate length of side US is 5.3 feet.

Step-by-step explanation:

Given,

Triangle STU in which,

m∠U = 90°,

m∠T = 47°,

Also, ST = 7.2 feet

By the law of sine,

$\frac{sin U}{ST}=\frac{sin T}{US}$

$sin U\times US=sin T\times ST$

$US=\frac{sin T\times ST}{sin U}$

By substituting the values,

$US=\frac{sin 47^{\circ}\times 7.2}{sin 90^{\circ}}=5.26574665166\approx 5.3$

Hence, The approximate length of side US is 5.3 feet.