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

Answer 1

i dont think this may be right but i think it is 401

Answer 2

Area of the triangle will be 161.70 cm²

Explanation:

In the figure attached, in ΔABC

m∠ABC = 23°

Adjacent side BC = 27.6 cm

and hypotenuse AC = 30 cm

Area of the triangle ABC =
`(1)/(2)* (\text{Height})* (\text{Base})`

=
`(1)/(2)(AB)(BC)`

By the sine rule,

sin23° =
`(AB)/(AC)`

AB = AC(sin23°)

= 30sin23°

= 30×(0.3907)

= 11.72 cm

Area of the triangle ABC =
`(1)/(2)* 11.72* 27.6`

= 11.72×13.8

= 161.736 cm²

≈ 161.7 cm²

Therefore, area of the triangle will be 161.70 cm².