In a right-angled triangle, the leg is 15 cm, and its projection onto the hypotenuse is 9 cm.

In a right-angled triangle, the leg is 15 cm, and its projection onto the hypotenuse is 9 cm. Find the hypotenuse, as well as the sine and cosine of the angle formed by this leg and the hypotenuse.

Leg a = 15 cm, projection k = 9 cm, hypotenuse c, leg b and angle B (between leg a and hypotenuse c). By metric ratios in a right-angled triangle:

a ^ 2 = k * c,

c = a ^ 2 / k = 15 ^ 2/9 = 25 (cm).

By the Pythagorean theorem:

b ^ 2 = c ^ 2 – a ^ 2 = 25 ^ 2 – 15 ^ 2 = 625 – 225 = 400,

b = 20 cm.

sin B = 20/25 = 4/5,

cos B = 15/25 = 3/5.