Dylan B. answered • 08/30/20
Math made easy!
When dealing with right triangles, you're most likely talking about trig functions, like sine (or sin), cosine (or cos), and tangent (or tan). A helpful tip for remembering how these relate to the parts of a right triangle is SOHCAHTOA, or what I was taught, "Some old hippie Came a hopping Through our alley." What SOHCAHTOA stands for is:
sinθ = opposite / hypotenuse
cosθ = adjacent / hypotenuse
tanθ = opposite / adjacent
What you need to do is look at the angle, here θ, and determine which is your opposite and adjacent. The adjacent side is the side that touches the angle, but isn't the hypotenuse, and the opposite side is the side directly opposite of the angle, and does not touch the angle. The hypotenuse is always the longest side of the triangle.
Using this info, we can say that a is the opposite side, and b is the adjacent side. Now you just need to use SOHCAHTOA to find out what these lengths are equal to using your angle θ.
For a, because it is the opposite side, we will use sine. Remember that your hypotenuse is given as 24, so we can plug in the information we have and solve for the unknown lengths:
sinθ = opposite / hypotenuse
= a / 24
a = 24sinθ
For b, because it is the adjacent side, we will use cosine.
cosθ = adjacent / hypotenuse
= b / 24
b = 24cosθ
And there you have it. a = 24sinθ, and b = 24cosθ
