Question

A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. What is the approximate area of the triangle?

Answer 1

$\Huge{\boxed{\pink{\mathbb{QUESTION}}}}$

A right triangle has one angle that measures 23°. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. What is the approximate area of the triangle?

$\Huge{\boxed{\purple{\mathcal{ANSWER}}}}$

$\bold{Given\:that,}$

One of the angle = 23°

Adjacent leg = 27.6 cm

Hypotenuse = 30 cm

$\bold{To\:find,}$

Area of the right triangle = ?

$\bold{We\:know\:that,}$

Area of a right-angled triangle = $\frac{1}{2} \times leg_{1} \times leg_{2}$

Here, the given quantities are,

Hypotenuse = 30 cm

$leg_{1}$ = 27.6 cm

$leg_{2}$ = ?

But, by using Pythagoras therom we can find out the length of $leg_{2}$.

$Hy^2 = AB^2 + BC^2$

$Hy^2 = leg_{1}^2 + leg_{2}^2$

$leg_{2}^2 = hy^2 - leg_{1}^2$

$leg_{2}^2 = (30)^2 - (27.6)^2$

$leg_{2}^2 = 138.24$

$leg_{2} = \sqrt{138.24}$

$leg_{2} = 11.76\:cm\:(approximately)$

Now, we've gotta the value of $leg_{2}$, and now we'll find the area of the triangle.

Area = $\frac{1}{2} \times leg_{1} \times leg_{2}$

Area = $\frac{1}{2} \times 27.6\:cm \times 11.76\:cm$

Area = $\frac{1}{2} (324.576\:cm^2)$

Area = $\frac{1}{\cancel{2}} {\cancel{(324.576)}}$

Area = $162.288\:cm^2$

Area = $162.29\:cm^2\:(approximately)$

$\huge{\boxed{\boxed{\boxed{\red{Area = 162.29\:cm^2}}}}}$