Question

Find the length of the side labeled x round to the nearest 10th

Answer 1

Trig problem here. We have 2 right triangles, the one on the left and on the right. They share one side. To find the length of this side, look at the left triangle. The hypotenuse is 44 and theta is 25, and since cos(theta)=adjacent/hypotenuse, cos(25)=adjacent/44 therefore the sidelength is 44cos(25). We are looking for x and now have an angle and a side for the righthand side right triangle so because tan(theta)=opposite/adjacent, tan(34)=opposite/(44cos(25)) therefore the opposite side is 44*cos(25)*tan(34)

Answer 2

You can solve for x by using trigonometry. However, only the angle opposite to x has been given. In order to get another length, find the altitude of the triangle. Use the length of the left side given to set up an equation like this. Let "y" equal the altitude temporarily.
Cos. 25 = y/44
Cos. 25 x 44 = y
0.9063 x 44 = y
39.8772 = y

Now that we have the altitude you can set up another equation for x.
Tan. 34 = x/39.8772
Tan. 34 x 39.8772 = x
0.6745 x 39.8772 = x
26.8971714 = x

Final Answer: x is approximately 26.9