In triangle ABC, angle C is 90 degrees, CH-height, BC = 5, cosine of angle A = 7/25. find BH.
| September 8, 2021 | education
Determine the sine of the angle BAC.
Sin2BAC + Cos2BAC = 1.
Sin2BAC = 1 – Cos2BAC = 1 – 49/625 = (625 – 49) / 625 = 576/625.
SinBAC = 24/25.
Let us determine the length of the hypotenuse AB.
SinBAC = BC / AB.
AB = BC / SinBAC = 5 / (24/25) = 125/24 cm.
Triangles ACB and СBN are similar in acute angle, then:
AB / BC = BC / BH.
BH = BC2 / AB = 25 / (125/24) = 600/125 = 4.8 cm.
Answer: The length of the BH segment is 4.8 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.
