In triangle ABC, angle C is 90 degrees, CH-height, AB = 18, sinA = 2/3. Find BH.

univerkov | August 4, 2021 | education

1. S – area ΔАВС.

2. We calculate the length of the BC leg through the sine ∠A:

BC: AB = sine ∠A = 2/3.

BC = AB x 2/3 = 18 x 2/3 = 12 units.

3. AC = √AB² – BC² = √18² – 12² = √324 – 144 = √180 = 6√5 units.

4. S = BC x AC / 2 = 12 x 6√5 / 2 = 36√5 units of measure².

5. According to another formula S = AB x CH / 2.

CH = 2S: AB = 2 x 36√5: 18 = 4√5 units.

6. VN = √BC² – CH² = √12² – (4√5) ² = √144 – 80 = √64 = 8 units.

Answer: the length of the VN segment is 8 units of measurement.

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