Question

QUICK WHO EVER GETS THIS RIGHT WILL GET BRAINLIEST AND 5 STARS
Given: △AKL, AK=9 m∠K=90°, m∠A=60° Find: Perimeter of △AKL Area of △AKL

Answer 1

We have been given a triangle AKL, with following information:

AK=9 m∠K=90°, m∠A=60°

In △AKL, $tan(A)=\frac{KL}{AK}$

$tan(60 ° ) =\frac{KL}{9}$

$\sqrt{3}=\frac{KL}{9}$

$9\sqrt{3}=KL$

In right angle  △AKL, we can apply Pythogorean theorem

$AL^2=AK^2+KL^2$

$AL^2=9^2+(9\sqrt{3})^2$

$AL^2=81+81*3$

$AL^2=81+243$

$AL^2=324$

AL=18

Area is given by formula:

$Area=\frac{1}{2}*(base)*(Altitude)$

$Area=\frac{1}{2}*(9\sqrt{3})*(18)$

$Area=81\sqrt{3}$

Perimeter is just sum of all sides

$Perimeter = 9+18+9\sqrt{3}$

$Perimeter = 27+9\sqrt{3}$