The height of a right-angled triangle, drawn from the vertex of the right angle, divides the hypotenuse

The height of a right-angled triangle, drawn from the vertex of the right angle, divides the hypotenuse into segments 1 cm and 3 cm long. Find the acute corners of this triangle.

1. A, B, C – the vertices of the triangle. ∠С = 90 °. CE – height. AE = 1 centimeter. BE = 3 centimeters.

2. We calculate the length of the height CE, which, according to the properties of a right-angled triangle, is calculated by the formula:

CE = √AE x BE = √1 x 3 = √3 centimeters.

3. We calculate the degree measure ∠А through its tangent. Tangent ∠A = CE: AE = √3. An angle whose tangent is √3 is 60 °. That is, ∠A = 60 °.

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

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