Question

In the right triangle shown,

∠
B
=
6
0

∠B=60

angle, B, equals, 60, degrees and
B
C
=
3 squared 3

Answer 1

The length of AB =
`x=6√(3)`

Explanation:

Given

• θ = m∠B = 60⁰

• BC =
  `3√(3)`

So we have to determine the length of AB which is Hypotenuse.

i.e. AB = Hypotenuse = x ?

so

Using the formula

Cos θ = Adjacent / Hypotenuse

Here:

• Adjacent = BC =
  `3√(3)`

so

Cos θ = Adjacent / Hypotenuse

`\cos \left(60^(\circ \:)\right)=(3√(3))/(x)` ∵ AB = Hypotenuse = x

`(1)/(2)x=3√(3)` ∵
`\cos \left(60^(\circ )\right)=(1)/(2)`

`x=6√(3)`

Therefore, the length of AB =
`x=6√(3)`