College Algebra & Trigonometry, 2018a

8.2. THE TRIGONOMETRIC RATIOS 353
Since we know the legs of the triangle, we can substitute these values for a and b
in the Pythagorean Theorem:
3 2 +5 2 = c 2
9+25=c 2
34 = c 2
√
34 = c
Now that we know the hypotenuse ( √ 34), we can determine the sin, cos and tan
for the angle θ.
sin θ = 3 √
34
cos θ = 5 √
34
tan θ = 3 5
Find sin θ, cos θ and tan θ for the given angle θ
θ
9
4
Again, in order to find the sin, cos and tan of the angle θ, we must find the missing
side of the triangle by using the Pythagorean Theorem. Since, in this case, we
know the hypotenuse and one of the legs, the value of the hypotenuse must be
substituted for c and the length of the leg we’re given can be substituted for either
a or b.