Question

Abc is an equilateral triangle. P is the point on side bc such that pc = 13 bc. If ab = 6 cm, then find ap.

Answer 1

Step-by-step explanation:

ΔABC  is an equilateral triangle so each side & each angle are equal i.e. AB=BC=AC=6 & ∠A=∠B=∠C=60°

PC = 1/3(BC) =1/3(6)=2

by cosine formula in ΔAPC

cas∠C = ac²+pc²- ap²

                2(ac)(pc)

cas60° = (6)²+(2)²-(ap)²

                    2(6)(2)

1/2 = 36+4-ap²

              24

1/2 = 40-ap²

            24

doing cross multiplection

24 = 2(40-ap²)

24 = 80 - 2ap²

24-80 = 2ap²

56/2 = ap²

28 = ap²

ap = √28

ap = 2√7

ap =5·291502622129181