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Anna007 [38]
3 years ago
14

Find the area of △LKJ.

Mathematics
1 answer:
nirvana33 [79]3 years ago
5 0

Answer:

A=600\: u^{2}

<u>The correct answer is letter c.</u>

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!

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