Question

In triangle STU, UT=5 and angleS=21. Find SU to the nearest tenth

Answer 1

13.0

Explanation:

The given angle is m<S=21.

The given side length UT=5 units.

This side length is opposite to the given angle.

Since we want to find SU, the adjacent side; we use the tangent ratio to obtain;

`\tan 21\degree=(opposite)/(adjacent)`

`\tan 21\degree=(5)/(SU)`

This implies that;

`SU=(5)/(\tan 21\degree)`

Therefore SU=13.025

The nearest tenth

SU=13.0

Answer 2

Hello!

The answer is:

The second option,

`SU=13.02=13`

Why?

We are working with a right triangle, it means that we can use the following trigonometric property:

`Tan(\alpha)=(Opposite)/(Adjacent)`

Which applied to our problem, will be:

`Tan(\alpha)=(TU)/(SU)`

We are given:

m∠S, equal to 21°

The side TU (opposite) equal to 5 units.

So, substituting and calculating we have:

`SU=(TU)/(Tan(\alpha))`

`SU=(5units)/(Tan(21\°))`

`SU=13.02=13`

Hence, the answer is the second option

`SU=13.02=13`

Have a nice day!