Find the area of the triangle with hypotenuse 8cm and one of the acute angle is 57°

From the above figure,

⇒ sin θ =

⇒ sin 57° =

From the sine table, sin 57° = 0.8387.

∴ 0.8387 =

∴ AB = 0.8387 × 8 = 6.7096 cm

Then cos θ =

⇒ cos 57° =

From the cosine table, cos 57° = 0.5446

∴ 0.5446 =

∴ BC = 0.5446 × 8 = 4.3568 cm

We know that Area of right angled triangle = 1/2 bh.

∴ Area of ΔABC = 1/2 × 4.3568 × 6.7096

= 14.616192

∴ Area of the triangle is 14.62 cm² (Approximately).