In triangle ABC, angle C is 90 degrees CH height, AC = 4, AH = √7. Find CosВ.

univerkov | December 30, 2020 | education

Since CH is the height, the triangle AСН is rectangular. Let’s apply the Pythagorean theorem:
AH ^ 2 + CH ^ 2 = AC ^ 2
(root of 7) ^ 2 + CH ^ 2 = 4 ^ 2
7 + CH ^ 2 = 16
CH ^ 2 = 9
CH = 3
cosB = sinA, so we find sinA from the ACН triangle:
sinA = CH / AC
sinA = 3/4
Hence, cosB = 3/4
Answer: cosB = 3/4

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