Question

Find the area of △LKJ.

Answer 1

Answer:

$A=600\: u^{2}$

The correct answer is letter c.

Step-by-step explanation:

The area equation of a triangle is given by:

$A=\frac{bh}{2}$  (1)

Where:

b is the base

h is the height

Let's find first the angle MJK (α), using the tangent definition.

$tan(\alpha)=\frac{24}{32}$

$\alpha=tan^{-1}(\frac{24}{32})$

$\alpha=36.9^{\circ}$

Now, if α = 37° then β (angle JLK) must be:

$37^{\circ} + \beta + 90^{\circ}=180^{\circ}$

$\beta=53^{\circ}$

Now, we can find the distance ML using again the tangent definition:

$tan(\beta)=\frac{24}{ML}$

$ML=\frac{24}{tan(53)}$

$ML=18$

The base of the triangle LKJ will be:

$b=32+ML=32+18=50$

Therefore, using equation (1) the area of △LKJ will be:

$A=\frac{50*24}{2}$

$A=600\: u^{2}$

The correct answer is c.

I hope it helps you!