In triangle ABC, angle C is 90 degrees, AC = 8, cos A = √7 / 4. Find the height CH.
| March 2, 2021 | education
Since the angle C is 90 °, the triangle is right-angled c AB, then its height is equal to leg BC. Let’s find the hypotenuse:
AB = AC / cos (A) = 8: √7 / 4 = 32 / √7.
By the Pythagorean theorem, we get:
BC ^ 2 = AB ^ 2 – AC ^ 2;
BC ^ 2 = 1024/7 – 64 = 9;
BC = 3.
Answer: the required height is 3.
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