In a right-angled triangle ABC, the height CD is built from the right angle C, the length of the height is 6 cm

| August 2, 2021 | education

In a right-angled triangle ABC, the height CD is built from the right angle C, the length of the height is 6 cm, the cosine of the angle BCD is 0.8. What is the hypotenuse of triangle ABC?

1. Considering that the cosine of the angle ВСD is equal to DC / ВС, we calculate ВС:

BC = 6: 0.8 = 7.5 cm.

2. Using the Pythagorean theorem, we calculate the length of the segment ВD:

ВD ^ 2 = ВС ^ 2 – СD ^ 2 = 7.5 ^ 2 – 6 ^ 2;

BD = √56.25 – 36 = √20.25 = 4.5 cm.

3. Using the theorem on the height, drawn from the vertex of the right angle, we calculate the length of the segment AD:

CD = √AD x BD;

CD ^ 2 = AD x BD;

AD = CD ^ 2: BD = 36: 4.5 = 8 cm.

4. We calculate the length of the hypotenuse AB:

AB = AD + BD = 8 + 4.5 = 12.5 cm.

Answer: the length of the hypotenuse AB is 2.5 cm.



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