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Do i use cos to solve these?
hi do u still need help?
hold on I got somebody else to take care of. Ill send you a person to help. @Arteam12
@Artteam12 could this be solved with cos?
umm this is tricky
You can use trig, but you can also use the known ratios of the lengths of sides of a 30-60-90 triangle.
Notice that both of the triangles are right triangles with a given 30-deg angle. That means the other angle must be a 60-deg angle. That makes both triangles 30-60-90 triangles. Ok so far?
In a 30-60-90 triangle, the hypotenuse is always twice the length of the shorter leg. Notice in the figure above, the hypotenuse is 2a and the short leg is a. If you know the short leg, multiply by 2 to get the hypotenuse. If you know the hypotenuse, divide by 2 to get the short leg.
Also, in a 30-60-90 triangle, the long leg is \(\sqrt 3\) times longer than the short leg. If you know the short leg, multiply by \(\sqrt 3\) to get the long leg. If you know the long leg, divide by \(\sqrt 3\) to find the short leg.
Now look at your problems. The first problem has a short leg measuring 10. What must the hypotenuse measure?
30 is an angle measure. You can;t use the Pythagorean theorem with angle measures. It only works with side lengths.
I wrote this above: "If you know the short leg, multiply by 2 to get the hypotenuse." In the first triangle, the short leg measures 10. What does the hypotenuse measure?
Good. In the first problem, the hypotenuse is y. We now know that y = 20. Which answer is correct?
Correct. A is the only answer that has y = 20, so A is it.
Now look at the second problem. The hypotenuse is given. It measures 28sqrt(3). y is the short leg. The short leg is half the hypotenuse. y is half of 28sqrt(3). Which answer has that value for y?