What is the value of in the triangle above? Round to the nearest hundredth.

Begin by filling in the missing angle for your triangle. Since a triangle has a total of degrees, you know that the missing angle is:

Draw out the figure:

Now, to solve this, you will need some trigonometry. Use the Law of Sines to calculate the value:

Solving for , you get:

Rounding, this is .

Begin by filling in the missing angle for your triangle. Since a triangle has a total of degrees, you know that the missing angle is:

Draw out the figure:

Now, to solve this, you will need some trigonometry. Use the Law of Sines to calculate the value:

Solving for , you get:

Rounding, this is .

Begin by filling in the missing angle for your triangle. Since a triangle has a total of degrees, you know that the missing angle is:

Draw out the figure:

This problem becomes incredibly easy! This is an isosceles triangle. Therefore, you know that is , because it is "across" from a degree angle—which matches the other degree angle!

We know that the perimeter is 36 inches, and one side is 12. This means, the sum of the lengths of the other two sides are 24. The ratio between the two sides is 3:5, giving a total of 8 parts. We divide the remaining length, 24 inches, by 8 giving us 3. This means each part is 3. We multiply this by the ratio and get 9:15, meaning the longest side is 15 inches.