Question

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

Answer 1

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`