shaleiah
  • shaleiah
@mathstudent55
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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shaleiah
  • shaleiah
Do i use cos to solve these?
Landon34
  • Landon34
hi do u still need help?
shaleiah
  • shaleiah
yes

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Landon34
  • Landon34
hold on I got somebody else to take care of. Ill send you a person to help. @Arteam12
Landon34
  • Landon34
@Artteam12
shaleiah
  • shaleiah
@Artteam12 could this be solved with cos?
anonymous
  • anonymous
umm this is tricky
mathstudent55
  • mathstudent55
You can use trig, but you can also use the known ratios of the lengths of sides of a 30-60-90 triangle.
mathstudent55
  • mathstudent55
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?
shaleiah
  • shaleiah
yes
mathstudent55
  • mathstudent55
|dw:1449773812190:dw|
mathstudent55
  • mathstudent55
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.
mathstudent55
  • mathstudent55
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.
shaleiah
  • shaleiah
alright
mathstudent55
  • mathstudent55
Now look at your problems. The first problem has a short leg measuring 10. What must the hypotenuse measure?
shaleiah
  • shaleiah
\[10^2+30^2=1000\]
mathstudent55
  • mathstudent55
30 is an angle measure. You can;t use the Pythagorean theorem with angle measures. It only works with side lengths.
mathstudent55
  • mathstudent55
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?
shaleiah
  • shaleiah
20
mathstudent55
  • mathstudent55
Good. In the first problem, the hypotenuse is y. We now know that y = 20. Which answer is correct?
shaleiah
  • shaleiah
b
shaleiah
  • shaleiah
sorry A
mathstudent55
  • mathstudent55
Correct. A is the only answer that has y = 20, so A is it.
mathstudent55
  • mathstudent55
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?

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