The leg and hypotenuse of a right triangle are 15 and 39. Find the height drawn to the hypotenuse

bystudin | May 31, 2020 | Education

AB – hypotenuse, BC – cathetus.
We find AC by the Pythagorean theorem:
AB2 = BC2 + CA2
39 ^ 2 = 15 ^ 2 + CA ^ 2
1521 = 225 + CA ^ 2
1296 = CA ^ 2
CA = 36
For triangle ABC:
sinA = CB / AB = 15/39 = 5/13
For triangle ACD:
sinA = CD / AC => CD = AC * sinA = 36 * 5/13 = 180/13 = 13 integers and 11/13
Answer: CD = 13 integers and 11/13

Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.