Question

A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm.

Answer 1

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

Answer 2

Answer:

Area of the triangle will be 161.70 cm²

Step-by-step 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 = $\frac{1}{2}\times (\text{Height})\times (\text{Base})$

= $\frac{1}{2}(AB)(BC)$

By the sine rule,

sin23° = $\frac{AB}{AC}$

AB = AC(sin23°)

     = 30sin23°

     = 30×(0.3907)

     = 11.72 cm

Area of the triangle ABC = $\frac{1}{2}\times 11.72\times 27.6$

= 11.72×13.8

= 161.736 cm²

≈ 161.7 cm²

Therefore, area of the triangle will be 161.70 cm².