Find the trigonometric ratios.
Right triangle A B C has right angle C with side A B equal to 53, B C equal to 28, and C A equal to 45.
There is no escape from memorizing the following:
sinθ = opposite/hypotenus
cosθ = adjacent/hypotenuse
tanθ = opposite/adjacent
cscθ = 1/sinθ
secθ = 1/cosθ
cotθ = 1/tanθ
you have all the numbers, make a sketch of your triangle and evaluate
actually, there is an escape.
Do about a hundred similar problems. After the first couple dozen, you will no longer have to look up the formulas; you will have learned them, not just memorized them.
Memorization will drive you crazy with trig. There are so many formulas which are similar, yet different!
Learn them live them, love them!
To find the trigonometric ratios for triangle ABC, we need to determine the ratios of the sides of the triangle.
Given that side AB is 53, side BC is 28, and side CA is 45, we can use these values to find the ratios.
The trigonometric ratios are defined as follows:
1. Sine (sin): It is the ratio of the length of the side opposite the angle to the length of the hypotenuse.
Therefore, sin(A) = BC / AB = 28 / 53.
2. Cosine (cos): It is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
Therefore, cos(A) = CA / AB = 45 / 53.
3. Tangent (tan): It is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
Therefore, tan(A) = BC / CA = 28 / 45.
Please note that the trigonometric ratios are specific to the angle A in this case. If you need to find the ratios for angle B or angle C, you would use the corresponding sides for those angles in the calculations.