Question

Find the area of △LKJ.

Answer 1

`A=600\: u^(2)`

The correct answer is letter c.

Explanation:

The area equation of a triangle is given by:

`A=(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)=(24)/(32)`

`\alpha=tan^(-1)((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)=(24)/(ML)`

`ML=(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=(50*24)/(2)`

`A=600\: u^(2)`

The correct answer is c.

I hope it helps you!