7.0k views
3 votes
Find the length of m

Anybody can help please?

Find the length of m Anybody can help please?-example-1
User Sboisse
by
8.8k points

1 Answer

4 votes

Answer:

m = 10

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) = (5 √(3) )/(m) }

We know that sin60° is √3/2


\displaystyle \large{ ( √(3) )/(2) = (5 √(3) )/(m) }

Multiply both sides by LCM which is 2m.


\displaystyle \large{ ( √(3) )/(2) (2m)= (5 √(3) )/(m) (2m)} \\ \displaystyle \large{ √(3) m=10 √(3) }

Divid both sides by √3 to isolate m.


\displaystyle \large{ ( √(3)m )/( √(3) ) = (10 √(3) )/( √(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) = (5 √(3) )/(m) }

We know that cos30° is √3/2


\displaystyle \large{ ( √(3) )/(2) = (5 √(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°.

User DonSeba
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories