the hypotenuse of that triangle is equal to the square root of the sum of the legs squared which is equal to sqrt(12^2 + 5^2) = sqrt(169) = 13.
see the diagram below:
in this triangle:
opposite side of the angle is equal to 5.
adjacent side of the angle is equal to -12.
hypotenuse of the triangle formed is equal to 13.
i called the angle T which stands for theta in this case.
sin(T) = opposite / hypotenuse = 5/13.
csc(T) = hypotenuse / opposite = 13/5
csc(T) is also equal to 1 / sin(t) = 1 / (5/13) = 13/5.
that's your answer.
csc(T) = 13/5
general formula used to find the hypotenuse:
c^2 = a^2 + b^2
c is the hypotenuse
a is one of the legs of the right triangle.
b is the other leg of the right triangle.
length of the hypotenuse is found by finding sqrt(c^2).
when graphing the angle and the right triangle formed:
x = a
y = b
h = c
formula becomes h^2 = x^2 + y^2
x is the side adjacent to the angle formed.
y is the side opposite to the angle formed.
h is the hypotenuse of the right triangle formed.
the angle formed is at the origin of the graph which is the intersection of the x and y axes.
