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? Round to the nearest tenth. Area of a triangle = bh 68.7 cm2 161.7 cm2 381.3 cm2 450.0 cm2

Answer 1

area of the truiangle is round off 162.15 cm^2

Answer 2

Area of triangle is $\bold{162.3 \ cm^2}$ approx.

Step-by-step explanation:

The area of a triangle is given as:

$\text{Area} =\frac{1}{2} b h$

Where,

b is base and h is height of the triangle

We are given the hypotenuse and base of the triangle. So, using the Pythagoras theorem we can get the height of the triangle as:

$30^{2}=27.6^{2}+h^{2}$

Rearranging the above equation we have:

$h^{2}=30^{2}-27.6^{2}$

Which can further be solved as:

$h^{2}=138.24 \ cm$

Which gives us the value of height as:

$h=11.76 \ cm$

Evidently from the formula mentioned above the area of the triangle can be given as:

$\frac{1}{2} b h=\frac{1}{2} \times 27.6 \times 11.76=162.3 \ \mathrm{cm}^{2}$