In a right-angled triangle, one of the legs is b and the included angle is B.

In a right-angled triangle, one of the legs is b and the included angle is B. Express the other leg, the opposite angle and the hypotenuse through b and B. Find their values if b = 10 B = 50.

Given:
right-angled triangle AСВ;
angle A = 90 degrees;
angle B = 50 degrees;
AB = 10.
Find AC, angle C, BC -?
Decision:
1) Consider a right-angled triangle ACB. The sum of the degree measures of the angles of a triangle is 180 degrees, that is, angle C + angle A + angle B = 180;
angle C = 180 – angle A – angle B;
angle C = 180 – 90 – 50;
angle C = 40;
2) tg B = AC / AB;
tg 50 = AC / 10;
AC = tg 50 * 10;
3) cos B = AB / BC;
cos 50 = 10 / BC;
BC = 10 / cos 50.
Answer: AC = tg 50 * 10; angle C = 40; BC = 10 / cos 50.