In triangle ABC, angle C is 90 degrees, CH is height, AB = 16, sine A = 3/4. Find AH.
February 10, 2021 | education
| Given:
ABC – right triangle;
Angle C = 90 degrees;
CH – height;
AB = 16;
sin A = 3/4;
Find AH.
Decision:
1) sin a = BC / AB;
From here we get that BC = AB * sin a = 16 * ¾ = 16/4 * 3 = 4 * 3 = 12;
2) Find the AC from the Pythagorean theorem.
AC = √ (AB ^ 2 – BC ^ 2) = √ (16 ^ 2 – 12 ^ 2) = √ (256 – 144) = √112 = √ (16 * 7) = √16 * √7 = 4 * √ 7;
2) From the formula AC ^ 2 = AB * AH we find AH.
In order to find the hypotenuse AB of the triangle ABC, we use the formula:
AH = AC ^ 2 / AB;
Substitute the known values into the formula and find AH.
AH = AC ^ 2 / AB = (4 * √7) ^ 2/16 = 16 * 7/16 = 16/16 * 7 = 1 * 7 = 7;
Answer: AH = 7.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.