Question

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

Answer 1

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:

$Tan(\alpha)=\frac{Opposite}{Adjacent}$

Which applied to our problem, will be:

$Tan(\alpha)=\frac{TU}{SU}$

We are given:

m∠S, equal to 21°

The side TU (opposite) equal to 5 units.

So, substituting and calculating we have:

$SU=\frac{TU}{Tan(\alpha)}$

$SU=\frac{5units}{Tan(21\°)}$

$SU=13.02=13$

Hence, the answer is the second option

$SU=13.02=13$

Have a nice day!

Answer 2

Answer:

13.0

Step-by-step 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;

$\tan 21\degree=\frac{opposite}{adjacent}$

$\tan 21\degree=\frac{5}{SU}$

This implies that;

$SU=\frac{5}{\tan 21\degree}$

Therefore SU=13.025

The nearest tenth

SU=13.0