How do you find the values of all six trigonometric functions of a right triangle ABC where C is the right angle, given a=7, b=24, c=25?

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Answer 1 · 2018-05-19T15:57:41

See below:

Side A: 7 opposite angle: 16.26°
Side B: 24 opposite angle: 73.74°
Side C: 25 opposite angle: 90°

Well it depends which angle you want the trig values of, let's look at angle $α$ $alpha$ (opposite side A):

opposite is: 7
adjacent is: 24
hypotenuse is: 25

$sin = \frac{opp}{hypot} = \frac{7}{25}$ $sin = "opp"/"hypot" = 7/25$

$cos = \frac{adj}{hypot} = \frac{24}{25}$ $cos = "adj"/"hypot" = 24/25$

$tan = \frac{opp}{adj} = \frac{7}{24}$ $tan = "opp"/"adj" = 7/24$

$sec = \frac{1}{cos} = \frac{25}{24}$ $sec = 1/"cos" = 25/24$

$csc = \frac{1}{sin} = \frac{25}{7}$ $csc = 1/"sin" = 25/7$

$cot = \frac{1}{tan} = \frac{24}{7}$ $cot = 1/"tan" = 24/7$