Find the unknown sides and angles of a rectangular triangle if one of the legs is 5 cm, and the adjacent angle is 55 °.

Given: Triangle ABC – rectangular;
angle A – straight;
AB = 5 cm;
angle B = 55 degrees;
Find: angle С, lengths of sides АС, ВС -?
Decision:
1) Consider a right-angled triangle ABC. Sides AB and AC – legs, BC – hypotenuse;
2) cos B = AB / BC;
cos 55 = 5 / ВС; (cos 55 = 0.574)
ВС = 5: cos 55;
BC = 5: 0.574;
BC = 8.7;
3) sin B = AC / BC;
sin 55 = AC / 8.7; (sin 55 = 0.819)
AC = sin 55 * 8.7;
AC = 0.819 * 8.7;
AC = 7.1 cm;
4) angle C = 180 – (angle A + angle B);
angle C = 180 – (90 + 55);
angle C = 180 + 145;
angle C = 35 degrees.
Answer: 35 degrees; 8.7 cm and 7.1 cm.