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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