Answer: 10 cosec (62°)
Step-by-step explanation:
The given triangle in the problem is a right triangle. This means that we can use SohCahToa to solve for the length of our hypotenuse (Line A to C).
** SohCahToa is a way for you to memorize special trigonometric functions that can be used:
Soh - Sin = Opposite / Hypotenuse
Cah - Cos = Adjacent / Hypotenuse
Toa - Tan = Opposite / Adjacent **
For this triangle, we can use the angle, 62°, to determine the hypotenuse. We will use x to represent the value between A and C. If you examine the sides of the triangle, you'll see that the side opposite of our angle is 10.
Because we have values that are located opposite to the angle and on the hypotenuse, we will use Sin(θ) = Opposite / Hypotenuse.
** θ represents your angle **
Sin(θ) = 10 / x
We want x by itself so you'll need to multiply x to both sides and then divide by sin(θ). This should give you the following: x = 10 / sin(θ)
Being that 1 / sin(θ) = cosec(θ), you can substitute 1 / sin (θ) for cosec(θ).
This would give you x = opposite •
cosec(θ) which is the same as x = 10 cosec (62°).
I apologize if I didn't explain that clearly enough :/ I hope it helps you out a lil bit though!
