A triangle ABC angle C = 90 degrees Hypotenuse AB is divided by the height СH. Drawn from the vertex
May 31, 2021 | education
| A triangle ABC angle C = 90 degrees Hypotenuse AB is divided by the height СH. Drawn from the vertex of the right angle into segments AH-18cm and BH-8cm. Find the height CH.
The tangent of an angle in a right-angled triangle is equal to the ratio of the lengths of the opposite to the adjacent leg.
Consider triangle AHC. In it we find the tangent of angle A:
tg (A) = CH / AH.
Let’s find what the angle BCH is equal to:
∠BCH = 90 ° – ∠ABC = 90 ° – (90 ° – ∠A) = ∠A.
Consider a triangle BCH. Find the tangent of the angle BCH:
tg (∠BCH) = BH / CH.
If the angles are equal, then the tangents are also equal. Equating the tangents, we get:
CH / AH = BH / CH;
CH2 = AH * BH;
CH = √ (AH * BH);
CH = √ (18 * 8);
CH = 12.
Answer: the height is 12 cm.
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.