In a right-angled triangle, the leg is 12.8 cm. The length of the height of the right angle dropped from the apex

In a right-angled triangle, the leg is 12.8 cm. The length of the height of the right angle dropped from the apex on the hypotenuse is 6.4 cm, find the largest of the acute angles of the triangle.

1. Let us introduce the designations for the vertices of the triangle ABC. The perpendicular drawn to the hypotenuse of BC will be denoted by AН. The apex angle A is 90 °.

2. In the triangle ABН, the perpendicular AH is a leg, the length of which is half the hypotenuse AB (12.8: 6.4 = 2). Therefore, the angle opposite which this leg is located is 30 °.

3. We calculate the value of another acute angle of the triangle:

180 ° – 90 ° – 30 ° = 60 °.

Answer: The larger angle of a right-angled triangle is 60 °.