Answer: 10 cosec 62
Explanation: You are given the opposite side, and need to find the hypotenuse. Remember SOHCAHTOA and their respective reciprocals. In this case you would either use Sin (opposite/hypotenuse) or Cosec (hypotenuse/opposite).
We'll try cosec first.
x represents the hypotenuse
cosec (62) = x/10
You want to get the x by itself
(10) Cosec (62) = x/10 (10)
(10) Cosec (62) = x
Multiplying x/10 by 10 cancel out the two 10s, and leaves x by itself. What you do to one side you do to the other.
10 Cosec (62) = x
10 Cosec (62) is the answer.
If this was incorrect, we would try with sin. Let's do that just to double check. (Remember sin=opposite/hypotenuse)
x still represents the hypotenuse.
Sin (62) = 10/x
You want x by itself
(x) Sin (62) = 10/x (x)
Multiplying x/10 by x cancels out both x's on the right side, but since what you do to one side you do to the other, an x is now multiplying the Sin (62)
(x) Sin (62)/Sin (62) = 10/Sin (62)
x= 10/Sin(62)
Dividing both sides by Sin (62) leaves x by itself.
So another correct answer would be
10/Sin (62)
However, this is not one of the answers provided, so the first problem we did is correct.
