Question

Question 7 A triangle with sides AB = 6, BC = 5, CA= 6. Find Cos A
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Answer 1

Answer:

1

Step-by-step explanation:

cos A= adjecent/hypotenuse

so cosA=AB/CA

AB=6 CA=6

THEN cosA=6/6=1

Answer 2

Answer:

The value of cos A = 0.83.

Step-by-step explanation:

• In this triangle two arms are equal and they are AB and CA. (AB = CA = 6).

        So their opposite angles will be equal (∠B = ∠C)

• The opposite angle of side AB is ∠C

        The opposite angle of side BC is ∠A

         The opposite angle of side CA is ∠B

• From the law of sin, we get: $\frac{AB}{sin C} = \frac{BC}{sin A} = \frac{CA}{sin B}$

       AB = CA = 6, BC = 5, sin B = sin C as ∠B = ∠C

     The above formula can be written as, $\frac{BC}{sin A} = \frac{CA}{sin B}$

                                                                    $\frac{5}{sin A} = \frac{6}{sin B}$    or, 5sinB = 6sinA

      In a triangle sum of all angles = 180°, so ∠A + ∠B + ∠C = 180°

                                                                          ∠A + 2∠B = 180°

                                                                          2∠B = 180° - ∠A

                                                                          ∠B = 90° - ∠$\frac{A}{2}$

Putting the value of ∠B in above equation,

 5sin(90° - ∠$\frac{A}{2}$) = 6sinA

 5cos(∠$\frac{A}{2}$) = 6(2$sin\frac{A}{2} cos\frac{A}{2}$)  [as sin(90°-x) = cosx and 2sinacosa= sin2a]

  5 = 12sin$\frac{A}{2}$           or, sin$\frac{A}{2}$ = 5/12      or, sin²$\frac{A}{2}$ = 25/144

• As we know, cos2a = 1 - 2sin²a

                             So, cosA = 1 - 2sin²$\frac{A}{2}$

                                            = 1 - 25/144 = 119/144 = 0.83

∴ The value of cos A = 0.83

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