Question

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

Answer 1

Answer:

$\large\boxed{A=89.6}$

Step-by-step explanation:

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

$A=\dfrac{leg\cdit leg}{2}$

We have:

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

Use tangent:

$tangent=\dfrac{opposite}{adjacent}$

$opposite=16,\ adjacent=x$

$\tan55^o\approx1.4281$

Substitute:

$\dfrac{16}{x}=1.4281$        convert the decimal to the fraction

$\dfrac{16}{x}=\dfrac{14281}{10000}$          cross multiply

$14281x=160000$            divide both sides by 14281

$x=\dfrac{160000}{14281}$

$x\approx11.2$

Calculate the area:

$A=\dfrac{(16)(11.2)}{2}=89.6$