Question

https://media.glynlyon.com/g_geo_2013/6/img_geou6a_46.gif

Answer 1

what would the longer side of the triangle be?

Answer 2

I know the pthagorean theorem and I can solve for x could omeone explain how I get the longer side of the triangle please?

Answer 3

You can't use the Pythagorean theorem on this.
There are 2 approaches.
1. You can use trigonometry. sin(30) = 4 / x Solve that for x
or
2. You recognize that that is a special triangle with angles of 30-60-90
Many people remember that the sides of these triangles are related in a special way in the ratio x - xroot(3) - 2x. In your example the 4 is the x and the hypotenuse is 2x or 2(4) which equals 8

Answer 4

So I don;t understand... does that mean x is 8?

Answer 5

I thought that it's proportional and since the opposite side of 30degrees is 4, 60 degrees would be 8, and 90 would have the opposite of 12.

Answer 6

the options are 2 square root 3, 4 square root 3, 8 square root 3, and 8.