Answer:
20
Step-by-step explanation:
Since we're dealing with a 60 degree angle you actually have 2 ways to figure this out!
Trigonometric way:
Recall what cos(theta) equals to, adj/hyp. We can set up an equation of
[tex]cos(60deg) = \frac{10}{hyp}[/tex], rearrange the equation to find hyp and solve!
[tex]hyp(cos(60deg)) = 10[/tex] (multiply both sides by hyp)
[tex]hyp = \frac{10}{cos(60deg) }[/tex]
Now, we could use a calculator but we should practice our basic trigonometric evaluating. Recall what cos(60 deg) is, it's 1/2. We can substitute that value back in and simplify!
[tex]hyp = \frac{10}{\frac{1}{2} }[/tex]
hyp = [tex]10(\frac{2}{1} )[/tex] (keep change flip method for division still applies here)
hyp = 20
Special Right Triangles (Basic Geometry):
If the bottom angle is 60 degrees then the top angle has to be 30, because the sum of the interior angles has to 180 which is the total angle measure of a triangle. Then, knowing the angles we identify that it's a 30-60-90 triangle thus we can apply its side ratio to find the hypotenuse! The side length opposite 30 degrees is x, the side length opposite of 60 is [tex]x\sqrt{3}[/tex] and the hypotenuse is 2x. So, knowing that the side length 10 is opposite of the 30 degree angle and that the 10 = x, we can easily figure that the hypotenuse, 2x is 20 (2*10).
Let me know if you have any questions!
