Respuesta :

Answer:

The correct answer is 151.

Step-by-step explanation:

Given,

In triangle ABC,

BC = a = 9 unit,

AB = c = 5 unit,

m∠B = 120°,

We have to find : b² or AC²,

By the cosine law,

[tex]b^2=a^2+c^2-2ac cosB[/tex]

[tex]=9^2+5^2-2\times 9\times 5\times cos 120^{\circ}[/tex]

[tex]=81+25-90\times -0.5[/tex]

[tex]=81+25+45[/tex]

[tex]=151[/tex]

Hence, the value of [tex]b^2[/tex] is 151.

Ver imagen parmesanchilliwack

Answer:

Option D) [tex]b^2 = 151[/tex]  

Step-by-step explanation:

We are given the following information in the question:

[tex]\triangle ABC\\\text{Side } a = 9\text{ units}\\\text{Side } c = 5\text{ units}\\\angle ABC = 120^{\circ}[/tex]

We have to find [tex]b^2[/tex]

The law of cosines state that if a, b and c are the sides of triangle and b is the side opposite to angle B, then,

[tex]b^2 = a^2 + c^2 - 2ac~\cos(B)[/tex]

Putting the values, we have,

[tex]b^2 = (9)^2 + (5)^2 - 2(9)(5)~\cos(120)\\\\b^2 = 81 + 25 - 90(-0.5)\\\\b^2 = 151[/tex]

Option D) [tex]b^2 = 151[/tex]

Ver imagen ChiKesselman