In a right-angled triangle ABC, the height AD divides the BC side into DC and BD where DC

| August 16, 2021 | education

In a right-angled triangle ABC, the height AD divides the BC side into DC and BD where DC is 18cm, AD is 24cm. Find AB and cos A

Let the value of the angle BAD of a right-angled triangle ABD be equal to X0, then the angle ABD = (90 – X) 0.

The angle ABC is straight, then the angle CBD = (90 – ABD) = (90 – (90 – X) = X0.

In right-angled triangles ABD and BCD acute angles are equal, then these triangles are similar.

Then AD / BD = BD / CD.

BD ^ 2 = AD * CD = 24 * 18 = 432.

In a right-angled triangle ABD, according to the Pythagorean theorem, we determine the length of the hypotenuse AB.

AB ^ 2 = AD ^ 2 + BD ^ 2 = 576 + 432 = 1008.

AB = 12 * √7 cm.

Determine the cosine of angle A.

CosA = AD / AB = 24/12 * √7 = 2 / √7 = 2 * √7 / 7.

Answer: The length of the AB side is 12 * √7 cm, CosA = 2 * √7 / 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.