In an isosceles triangle ABC with a base BC, the length of the lateral side and the length of the height drawn to the lateral side are given. AB = 29, CH = 20. Find the length of the side BC if it is known that the angle at the vertex A is obtuse.
Since angle A is obtuse, the height CH is drawn to the continuation of side AB.
The ABC triangle is isosceles, then AC = AB = 29 cm.
In a right-angled triangle ACH, according to the Pythagorean theorem, we determine the length of the segment AH.
AH ^ 2 = AC ^ 2 – CH ^ 2 = 29 ^ 2 – 20 ^ 2 = 841 – 400 = 441.
AH = 21 cm.
Then the length of the segment BH = AB + AH = 29 + 21 = 50 cm.
From the right-angled triangle ВСН, according to the Pythagorean theorem, we determine the length of the base ВС.
BC ^ 2 = BH ^ 2 + CH ^ 2 = 50 ^ 2 + 20 ^ 2 = 2500 + 400 = 2900.
BC = 10 * √34 cm.
Answer: The length of the base of the BC is 10 * √29 cm.
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