What is the area of the figure. please help show steps

Question

asked Aug 17, 2020 111k views

1 Answer

Alsk · Answer 1 · 2020-08-23T23:21:30+0000

Answer:
$143.99\ ft^2$

Explanation:

We need to find the lenght AC and BC of the triangle by applying these identities:

$cos\alpha=(adjacent)/(hypotenuse) \\\\sin\alpha=(opposite)/(hypotenuse)$

Then, AC is:

$sin(45\°)=(AC)/(24)\\\\AC=24*sin(45\°)\\\\AC=16.97\ ft$

And BC is:

$cos(45\°)=(BC)/(24)\\\\BC=24*cos(45\°)\\\\BC=16.97\ ft$

The area will be:

A=(AC*BC)/(2)

Substituting values, we get:

$A=((16.97\ ft)(16.97\ ft))/(2)=143.99\ ft^2$