In a right-angled triangle, the hypotenuse is 15 cm and the legs are 9 cm 12 cm

In a right-angled triangle, the hypotenuse is 15 cm and the legs are 9 cm 12 cm Find a) the cosine of a larger acute angle b) the sum of the cosines of acute angles

Given: right-angled triangle ABC;

angle C = 90;

hypotenuse AB = 15 centimeters;

AC = 9 centimeters;

BC = 12 centimeters.

Find: a) the cosine of a larger acute angle; b) the sum of the cosines of acute angles -?

Solution:

Consider a right-angled triangle ABC.

a) Opposite the larger side is the larger angle. Then angle A is greater than angle B.

The cosine of the angle in a right-angled triangle is equal to the ratio of the adjacent leg to the hypotenuse. Hence:

cos A = AC / AB;

cos A = 5/15;

cos A = 1/3.

b) cos B = BC / AB;

cos B = 12/15;

cos B = 4/5.

cos B + cos A = 1/3 + 4/5 = 5/15 + 12/15 = 17/15 = 1 2/15.

Answer: a) cos A = 1/3; b) 1 2/15.