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

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

1. Vertices of the triangle – A, B, C. ∠A = 90 °. AH = 5√3 centimeters – height drawn to

hypotenuse. CH = 15 centimeters – projection of the AC leg onto the hypotenuse.

2. We calculate the value of ∠С through its tangent:

AH / CH = tangent ∠C = 5√3: 15 = √3 / 3.

∠С = 30 °.

3. We calculate the value of ∠B, taking into account that the total value of the angles of the triangle is 180 °:

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

Answer: acute angles of the triangle ∠В = 60 °, ∠С = 30 °.