Question

Find the length of m

Anybody can help please?

Answer 1

Answer:

m = 10

Step-by-step explanation:

We are going to use sine ratio as sine ratio is opposite to hypotenuse.

We know the value of opposite which is 5√3

The value of hypotenuse is m which is unknown.

Therefore:-

$\displaystyle \large{ \sin(60 \degree) = \frac{5 \sqrt{3} }{m} }$

We know that sin60° is √3/2

$\displaystyle \large{ \frac{ \sqrt{3} }{2} = \frac{5 \sqrt{3} }{m} }$

Multiply both sides by LCM which is 2m.

$\displaystyle \large{ \frac{ \sqrt{3} }{2} (2m)= \frac{5 \sqrt{3} }{m} (2m)} \\ \displaystyle \large{ \sqrt{3} m=10 \sqrt{3} }$

Divid both sides by √3 to isolate m.

$\displaystyle \large{ \frac{ \sqrt{3}m }{ \sqrt{3} } = \frac{10 \sqrt{3} }{ \sqrt{3} } } \\ \displaystyle \large{ m = 10}$

And we're done! The value of m is 10.

Alternative Solutions

If we do not want to use sin60°, we can use cos30°.

Focus the 30°, since for 30°, 5√3 is adjacent and m is hypotenuse.

cosine ratio is adjacent to hypotenuse.

Therefore:-

$\displaystyle \large{ \cos(30 \degree) = \frac{5 \sqrt{3} }{m} }$

We know that cos30° is √3/2

$\displaystyle \large{ \frac{ \sqrt{3} }{2} = \frac{5 \sqrt{3} }{m} }$

Notice something? Both equations when we use sin60° and cos30° are same. This is called a co-function.

Since sin60° = cos30°, both methods work.

If we do not want to use sin60°, you can use cos30°.