One of the corners of a right-angled triangle is 47 degrees.

One of the corners of a right-angled triangle is 47 degrees. Find the angle between the hypotenuse and the median drawn from the top of the right angle.

1. The vertices of the triangle A, B, C. ∠C = 90 °. ∠А = 47 °. SC is the median. ∠АКС – the angle between the hypotenuse and the median.

2. According to the properties of a right-angled triangle, the length of the median drawn from the vertex of the right angle to the hypotenuse is equal to its half. That is, CК = 1 / 2AB.

3. The median divides the hypotenuse into two equal lengths AK and BK. Hence,

AK = SK, that is, triangle ACK is isosceles.

4. In an isosceles triangle, the angles at the base are equal, that is, ∠САK = ∠ACK = 47 °.

5. We calculate the degree measure of the required ∠АКС:

∠АКС = 180 ° – (∠САK + ∠АСК) = 180 ° – (47 ° + 47 °) = 86 °.

Answer: ∠АКС = 86 °.