Question

@mathstudent55

Answer 1

Do i use cos to solve these?

Answer 2

hi do u still need help?

Answer 3

yes

Answer 4

hold on I got somebody else to take care of. Ill send you a person to help. @Arteam12

Answer 5

@Artteam12

Answer 6

@Artteam12 could this be solved with cos?

Answer 7

umm this is tricky

Answer 8

You can use trig, but you can also use the known ratios of the lengths of sides of a 30-60-90 triangle.

Answer 9

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?

Answer 10

yes

Answer 11

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.

Answer 12

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.

Answer 13

alright

Answer 14

Now look at your problems.
The first problem has a short leg measuring 10.
What must the hypotenuse measure?

Answer 15

\[10^2+30^2=1000\]

Answer 16

30 is an angle measure.
You can;t use the Pythagorean theorem with angle measures. It only works with side lengths.

Answer 17

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?

Answer 18

20

Answer 19

Good.
In the first problem, the hypotenuse is y.
We now know that y = 20.
Which answer is correct?

Answer 20

b

Answer 21

sorry A

Answer 22

Correct. A is the only answer that has y = 20, so A is it.

Answer 23

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?