Question

Show that a = n, where n is an integer.
What is the value of n?

Answer 1

n = 30

Explanation:

For this question, use the cosine law formula:

`a=√(c^2+b^2-2cb*cosA) \\a=\sqrt{(√(6))^2+(4√(3))^2-2(√(6))(4√(3))*cos45 }\\a =\sqrt{6+48-(8√(18))*(√(2) )/(2) }\\a=\sqrt{54-(8√(36) )/(2) }\\a=√(54-24)\\a=√(30)`

If a =
`√(n)`, then n must be 30

Answer 2

n = 30

Explanation:

Since it is not a right-angle triangle, you will need to use sine or cosine rule;

We have two side lengths and the angle between, this means you need to use the cosine rule:

a² = b² + c² - 2bc.cosA

`{a}^(2) = ({4 √(3) })^(2) + {( √(6) )}^(2) - 2( 4√(3))( √(6) ). \cos(45) \\ {a}^(2) = 48 + 6 - 8 √(18)(0.707...) \\ {a}^(2) = 54 - 24 \\ {a}^(2) = 30 \\ a = √(30)`