Question

Find the area of the right triangle with hypotenuse $20cm$ and one of the acute angle is ${48}^{\circ }$

Answer 1

Let $△ABC$ is the right angle triangle, right angled at $B$ & $\angle C=48°$

Now,

$\Rightarrow \sin 48°=\frac{AB}{AC}=\frac{AB}{20}$

$\Rightarrow AC=20\sin 48°=20\times 0.7431$

$\Rightarrow AC=14.862cm$

Again,

$\Rightarrow \cos 48°=\frac{BC}{AC}=\frac{BC}{20}$

$\Rightarrow BC=20\times \cos 48°=20\times 0.6691$

$\Rightarrow BC=13.382$

Now, area $△ABC=\frac{1}{2}\times base\times height$

$=\frac{1}{2}\times 13.382\times 14.862$

$=99.42{cm}^2$

Hence the answer is $99.42{cm}^2.$