the length of the side AB of the triangle shown is 13 m 1127

the length of the side AB of the triangle shown is 13 m 11.27 m 9.22 m 8.95 m 6.48 m the length of the side AB of the right triangle shown is 12.6 m 11.8 m 10.5 m 9.24 m

Solution

24. Referring the provided figure :

We have in ABC,
ACB = 180 – 60 = 120° (by linear pair property)

Now in ABC, applying Cosine law of triangles we have,

AB² = BC² + AC² – 2*BC*AC*Cos(c)
AB² = 6² + 7² – 2*6*7*Cos(120°)
AB² = 85 – 2*42*(-1/2)
AB² = 85 + 42
AB = 127

AB = 11.27 m

25. Referring the provided figure :

We have ABC = 70° (alternate interior angles)

and, Sin B = AC/AB
or Sin(70°) = 8 / AB

= 0.9397

So, AB = 8 / 0.9397

= 8.513

or AB = 8.51 m