The hypotenuse AB of the right-angled triangle ABC is 500 mm, the sine A is 7/25, the cosine is 24/25.

The hypotenuse AB of the right-angled triangle ABC is 500 mm, the sine A is 7/25, the cosine is 24/25. Find the area of the triangle ABC.

1. To find the sine of an angle, you need to take the leg opposite this angle and divide by the hypotenuse, and to find the cosine, you need to take the leg that belongs to the angle, and divide by the hypotenuse, we get two equations:
x: 500 = 7/25 and y: 500 = 24/25
x = 140 – one leg
y = 480 – second leg.
2.To find the area, you need to multiply the legs and divide by 2.
(140 * 480) / 2 = 28800 mm2 or 288 cm2.
Answer: 28800 mm2 or 288 cm2.