In a right-angled triangle ABC, angle C = 90 degrees, AB = √2 AC, BC = 6 Find the height of CH.
| September 7, 2021 | education
Consider triangle ABC and find the sine of angle B. sin B = AC / AB, AB = √2 * AC, sin B = AC / (√2 * AC) = 1 / √2. Consider a right-angled triangle BCH (angle H of a straight line). Find the sine of angle B: sin B = CH / BC. Substitute the value sin B = 1 / √2 and BC = 6. We get CH / 6 = 1 / √2, CH = 6 / √2
Answer: CH = 6 / √2
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