Question

Consider the figure shown below, find the value of g ​

Answer 1

Given:

A figure of a triangle.

To find:

The value of g.

Solution:

Law of Cosines:

$a^2=b^2+c^2-2bccosA$

Using the Law of Cosines for the given triangle, we get

$g^2=8^2+7^2-2(8)(7)cos(65^\circ)$

$g^2=64+49-112(0.4226)$

$g^2=113-47.3312$

$g^2=65.6688$

Taking square root on both sides.

$g=\sqrt{65.6688}$

$g=8.10363$

$g\approx 8.10$

Therefore, the value of g is about 8.10 units.