Question

Find the area of the triangles round to the tenth. Show steps please!

Answer 1

`\large\boxed{A=89.6}`

Explanation:

It's the right triangle. The formula of an area of a right triangle:

`A=(leg\cdit leg)/(2)`

We have:

`leg=x\\leg=16\\\text{and the angle}\ \alpha=55^o`

Use tangent:

`tangent=(opposite)/(adjacent)`

`opposite=16,\ adjacent=x`

`\tan55^o\approx1.4281`

Substitute:

`(16)/(x)=1.4281` convert the decimal to the fraction

`(16)/(x)=(14281)/(10000)` cross multiply

`14281x=160000` divide both sides by 14281

`x=(160000)/(14281)`

`x\approx11.2`

Calculate the area:

`A=((16)(11.2))/(2)=89.6`