In a right-angled triangle, the hypotenuse is 5 dm and the acute angle is φ, find the adjacent leg and hypotenuse.

Let the angle C in the triangle ABC be straight, and AB the hypotenuse equal to 5 dm, angle B – acute and equal to φ. Find the adjacent legs:

AC = AB * sin φ,

AC = 5 * sin φ dm.

Since triangle ABC is rectangular, we find the angle A:

∠А = 90 ° – ∠В;

∠А = 90 ° – φ.

Now we will find the BC leg:

BC = AB * sin (90 ° – φ);

ВС = 5 * sin (90 ° – φ) dm.

Answer: the adjacent legs are equal: AC – 5 * sin φ dm, BC – 5 * sin (90 ° – φ) dm.