Question

question in △efg, e = 370 cm, f = 880 cm and ∠g = 159°. find the length of g, to the nearest centimeter. answer attempt 1 out of 2 submit answer watch video show examples

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula for finding side $g$ in $\triangle EFG$ is $g^{2}=e^{2}+f^{2}-2ef\cos G$. Given $e = 370$ cm, $f = 880$ cm and $G=159^{\circ}$. First, calculate the values of $e^{2}$, $f^{2}$ and $2ef\cos G$.
$e^{2}=370^{2}=136900$, $f^{2}=880^{2}=774400$, and $2ef\cos G=2\times370\times880\times\cos(159^{\circ})$. Since $\cos(159^{\circ})\approx - 0.9336$, then $2\times370\times880\times(-0.9336)=2\times370\times880\times(- 0.9336)\approx - 610997.76$.

Step2: Calculate $g^{2}$

$g^{2}=e^{2}+f^{2}-2ef\cos G=136900 + 774400-(-610997.76)=136900+774400 + 610997.76=1522297.76$.

Step3: Find $g$

$g=\sqrt{1522297.76}\approx1234$ cm.

Answer:

$1234$ cm