Question

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Answer 1

Answer:

Angle B = 106.6 degrees

Step-by-step explanation:

b^2= a^2+c^2-2*a*c*cosB

9*9 = 4*4 + 7*7 - 2*7*4*cosB

81= 16+49-56cosB           Subtract 16 and 49 from both sides

16= -56cosB           Divide by -56 on both sides.

cosB= -16/56         Take the arccosine of both sides

B=arccos(-16/56)                    

B= 106.6

Answer 2

Answer:

B. 106.6

Step-by-step explanation:

To solve for angle B, we can use the law of cosines.

Recall that the law of cosines states $b^2=a^2+c^2-2ab*cos(B)$

When this is solved for angle B, we get $B=cos^{-1}( \frac{a^2+c^2-b^2}{2ac} )$

In this triangle, $a=7, b=9, c=4$

Now, we can plug these numbers into our equation and then simplify to get B.

$B=cos^{-1}( \frac{7^2+4^2-9^2}{2(7)(4)} )\\\\B=cos^{-1}( \frac{49+16-81}{56} )\\\\B=cos^{-1} (\frac{-16}{56} )\\\\B=106.602\\\\B=106.6$