# The height BD of right-angled triangle ABC is 24 cm and cuts off a segment DC equal to 18 cm

September 28, 2021 | education

| **The height BD of right-angled triangle ABC is 24 cm and cuts off a segment DC equal to 18 cm from hepotenuse AC Find AB and cosine of A**

1. We calculate the length of the segment AH, applying the formula for calculating the length of the height BH, drawn from the vertex of an angle equal to 90 °:

BH = √AH x CH.

BH² = AH x CH.

AH = BH²: CH = 24²: 18 = 576: 18 = 32 centimeters.

2. We calculate the length of the side AB of the given triangle, which in the right-angled triangle ABH is the hypotenuse:

AB = √АH² + BH² (by the Pythagorean theorem).

AB = √32² + 24² = √1024 + 576 = √1600 = 40 centimeters.

3. Cosine ∠A = AH: AB = 32: 40 = 0.8.

Answer: AB = 40 centimeters, cosine ∠A = 0.8.

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