Question

Find the length of ST. Round your answer to the nearest tenth of an inch.

Answer 1

7.1

Explanation:

Once again we can use trig ratios to solve for ST

First we must recall the trig function

Sin = Opposite over Hypotenuse

Cos = Adjacent over Hypotenuse

Tan = Opposite over Adjacent

We are given the measure of an angle and the length of the hypotenuse

Of the given angle we need to find the adjacent side length

When working with the hypotenuse and adjacent we use trig function cosine

That being said we want to create an equation ( remember cos = adjacent over hypotenuse ) ( let ST = x)

`cos(42)=(x)/(9.5)`

now we solve for x

Step 1 multiply each side by 9.5

`cos(42)*9.5=9.5cos(42)=7.059875842\\(x)/(9.5) *9.5=x`

we're left with x = 7.059875842

Finally we round to the nearest tenth and get that the answer is 7.1