In a right-angled triangle KPF, the height KD of triangle KPF is 24 cm and cuts off a segment DF equal to 18 cm from the hypotenuse PF, find KP and cos of the angle P
Since the height KD is drawn to the hypotenuse from a right angle, then:
KD ^ 2 = PD * DF, then:
PD = KD ^ 2 / DF = 576/18 = 32 cm.
Then the length of the hypotenuse is PF = PD + DF = 32 + 18 = 50 cm.
From the right-angled triangle KPD we determine the length of the hypotenuse KP.
KP ^ 2 = PD ^ 2 + KD ^ 2 = 32 ^ 2 + 24 ^ 2 = 1024 + 576 = 1600.
KP = 40 cm.
Determine the cosine of the angle KPF.
CosKPF = KP / PF = 40/50 = 4/5.
Answer: The length of the side of the KP is 40 cm, CosP = 4/5.
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.