In a right-angled triangle ABC from the vertex of the right angle C, the median CD is drawn to the hypotenuse

| August 7, 2021 | education

In a right-angled triangle ABC from the vertex of the right angle C, the median CD is drawn to the hypotenuse AB, and the values of the angles BDC and ADC are related as 4: 5 find the value of the angle A

Let the value of the angle ADC = 5 * X0, then, by condition, the value of the angle BDC = 4 * X0.

The sum of the angles ADC and BDC gives the unfolded angle ADB, then:

5 * X + 5 * 4 = 180.

X = 180/9 = 20.

Angle ADC = 5 * 20 = 100.

Since triangle ABC is rectangular, and point D is the middle of the hypotenuse AB, a circle can be described around the triangle, the center of which will be point D.

Then the segments AD, CD and BD are the radii of the circle, then the triangle ADC is isosceles and the angle DAC = DСА.

Then 2 * DAC + ADC = 180.

2 * DAC = 180 – 100 = 80.

Angle DAC = 80/2 = 40.

Answer: Angle A of the triangle is 40.



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