Question

In ΔSTU, the measure of ∠U=90°, ST = 9.7 feet, and US = 4 feet. Find the measure of ∠T to the nearest degree.

Answer 1

We have been given that in ΔSTU, the measure of ∠U=90°, ST = 9.7 feet, and US = 4 feet. We are asked to find the measure of ∠T to the nearest degree.

First of all, we will draw a right triangle using our given information.

We can see that US is opposite to angle T and ST is hypotenuse of right triangle.

We know that sine relates opposite side of right triangle to hypotenuse.

`\sin=\frac{\text{Opposite}}{\text{Hypotenuse}}`

`\sin(\angle T)=(US)/(ST)`

`\sin(\angle T)=(4)/(9.7)`

Now we will use arcsin to solve for measure of angle T as:

`\angle T=\sin^(-1)((4)/(9.7))`

`\angle T=24.353873017978^(\circ)`

Upon rounding to nearest degree, we will get:

`\angle T\approx 24^(\circ)`

Therefore, the measure of angle T is approximately 24 degrees.