The height BD of a right-angled triangle ABC is 24 cm and cuts off a segment DC

The height BD of a right-angled triangle ABC is 24 cm and cuts off a segment DC equal to 18 cm from the hypotenuse AC. Find AB Cos of angle A.

Given:
right-angled triangle AB;
ВD – height;
ВD = 24 cm;
DC = 18 cm.
find AB, Cos of angle A -?
Decision:
1) ВD = √СD * DA;
ВD ^ 2 = СD * DA;
DA = BD ^ 2 / CD;
DA = 24 ^ 2/18;
DA = 576/18;
DA = 32 cm;
2) CA = CD + DA;
CA = 32 + 18 = 50 (cm);
3) Consider a right-angled triangle ВDА. By the Pythagorean theorem:
BA ^ 2 = BD ^ 2 + DA ^ 2;
BA ^ 2 = 24 ^ 2 + 32 ^ 2;
BA ^ 2 = 576 + 1024;
VA ^ 2 = 1600;
VA = 40 cm;
4) Cos of angle A = VA / CA;
Cos of angle A = 40/50;
Cos of angle A = 4/5.
Answer: 40 centimeters; Cos of angle A = 4/5.