Find the acute corners of a right-angled triangle if the height drawn to the hypotenuse is 5 root 3 cm

Find the acute corners of a right-angled triangle if the height drawn to the hypotenuse is 5 root 3 cm, and the projection of one of the legs is 15 cm.

1. The vertices of the triangle A, B, C. ∠C = 90 °. CH = 5√3 cm – height (drawn to the hypotenuse AB). BH = 15 cm.

2. The height drawn from the top of the right angle to the hypotenuse is calculated by the formula:

CH = √ВН x AН.

3. We use this formula to calculate the length of the segment AH.

CH² = ВН x AН.

AH = CH²: BH = (5√3) ²: 15 = 75: 15 = 5 cm.

4. CH: AH = tangent ∠A.

5√3: 5 = √3.

The tangent angle of which √3 is 60 °, that is, ∠A = 60 °.

5.∠В = 180 – ∠С – А = 180 ° – 90 ° – 60 ° = 30 °.

Answer: ∠А = 60 °, ∠В = 30 °.