∆ABC is an equilateral triangle. Point P is on base BC such that PC = 1/3 BC. If AB = 12 cm, find AP​

Step-by-step explanation:

It is given that ABC is an equilateral triangle, then AB=BC=AC=6cm and ∠A=∠B=∠C=60°, then according to question, PC=\frac{1}{3}BC

therefore PC=2 cm.

Now, using the cosine formula in ΔAPC, we have

cos∠C= \frac{AC^{2}+PC^{2}-AP^{2}}{2(AC)(PC)}

cos60°=\frac{6^{2}+2^{2}-AP^{2}}{2(6)(2)}

\frac{1}{2}=\frac{40-AP^{2}}{24}

AP^{2}=40-12

AP^{2}=28

AP=2\sqrt{7}cm

step-by-step explanation:

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.