Question

In triangle ABC, AB = 2x cm, AC = x cm, BC = 21 cm and angle BAC = 120°.
Calculate the value of x.

Answer 1

Step-by-step explanation:

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Answer 2

The value of x is √63cm

GIVEN

ABC is a triangle.

AB = 2x cm

AC = x cm

BC = 21 cm

∠BAC = 120°

TO FIND

The value of x

SOLUTION

We can simply solve the above problem as follows;

In ΔABC

AB = a = 2x cm

AC = b = x cm

BC = c = 21 cm

∠BAC = 120°

Applying the cosine theorem in ΔABC

$\cos(a) = \frac{ {b}^{2} + {c}^{2} - {a}^{2} }{2bc}$

Putting the values in the above formula we get;

$\cos(120) = \frac{ {x}^{2} + {2x}^{2} - {21}^{2} }{2x \times 2x}$

Putting the value of Cos 120 is -1/2

$- \frac{1}{2} = \frac{5 {x}^{2} - 441 }{ {4x}^{2} }$

-4x² = 10x² - 882

14x² = 882

x² = 882/14 = 63

x = √63

Hence, The value of x is √63cm

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