Question

In the right triangle shown,

Answer 1

Answer:

The length of AB = $x=6\sqrt{3}$

Step-by-step explanation:

Given

• θ = m∠B = 60⁰

• BC = $3\sqrt{3}$

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 = $3\sqrt{3}$

so

Cos θ = Adjacent / Hypotenuse

$\cos \left(60^{\circ \:}\right)=\frac{3\sqrt{3}}{x}$            ∵ AB = Hypotenuse = x

$\frac{1}{2}x=3\sqrt{3}$          ∵ $\cos \left(60^{\circ }\right)=\frac{1}{2}$

$x=6\sqrt{3}$            

Therefore, the length of AB = $x=6\sqrt{3}$