In a right-angled triangle ABC, the hypotenuse AB = 4 dm and the angle A = 42.

In a right-angled triangle ABC, the hypotenuse AB = 4 dm and the angle A = 42. Find its unknown acute angle and legs with an accuracy of 0.1 dm.

The sum of the acute angles in a right-angled triangle is 90 °, so the angle B = 90 – 42 = 48 °.
Now let’s find the legs:
BC = AB * sinA = 4 * sin42 ° = 4 * 0.7 = 2.8 dm
AC = AB * cos A = 4 * cos42 = 4 * 0.7 = 2.8 dm
Answer: angle B = 48 °, BC = AC = 2.8 dm