Point H is the base of the height drawn from the vertex of the right angle B of the triangle ABC to the hypotenuse AC. Find AB if AH = 10 and AC = 40
Find the length of the segment CH:
AC = AH + CH;
10 + CH = 40;
CH = 40-10;
CH = 30 conventional units.
The length of the height of a right-angled triangle, drawn to the hypotenuse, can be found by the formula:
BH² = AH * CH.
Substitute the data according to the value condition and find the length of the height:
BH = √ (10 * 30) = √300 (conventional units).
From △ AHB, by the Pythagorean theorem, we find AB (AB is the hypotenuse, AH and BH are legs):
AB² = AH² + BH²;
AB = √ (AH² + BH²);
AB = √ (10² + (√300) ²);
AB = √ (100 + 300);
AB = √400;
AB = 20 conventional units.
Answer: AB = 20 conventional units.
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