In triangle ABC, the angle C is 90 °. CH is the height, AC = 5, AH = 3. Find cos B
April 10, 2021 | education
| Given:
ABC – right triangle;
Angle C = 90 degrees;
CH – height;
AC = 5;
AH = 3;
Find cos b.
Decision:
1) From the formula AC ^ 2 = AB * AH we find the hypotenuse AB.
In order to find the hypotenuse AB of the triangle ABC, we use the formula:
AB = AC ^ 2 / AH;
Substitute the known values into the formula and find the hypotenuse AB.
AB = AC ^ 2 / AH = 5 ^ 2/3 = 25/3;
2) From the formula cos b = AC / AB we find cos b.
cos b = 5 / (25/3) = 5/1 * 3/25 = 5/25 * 3 = 1/5 * 3 = 3/5 = 0.6;
As a result, we got that cos b = 0.6.
Answer: cos b = 0.6.
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