Answer:
[tex]\cos(A) = \frac{60}{61}[/tex]
Step-by-step explanation:
Given
[tex]\tan(A) = \frac{11}{60}[/tex]
[tex]0 \le A \le 90[/tex] --- First Quadrant
Required
Find cos(A)
The tan of an angle is:
[tex]\tan(A) = \frac{Opposite}{Adjacent}[/tex]
and
[tex]\tan(A) = \frac{11}{60}[/tex]
By comparison:
[tex]Opposite = 11[/tex]
[tex]Adjacent = 60[/tex]
So, the hypotenuse is:
[tex]Hypotenuse^2 = Adjacent^2 + Opposite^2[/tex]
[tex]Hypotenuse^2 = 60^2 + 11^2[/tex]
[tex]Hypotenuse^2 = 3721[/tex]
Take square roots
[tex]Hypotenuse = \sqrt{3721[/tex]
[tex]Hypotenuse = 61[/tex]
The cosine of an angle is:
[tex]\cos(A) = \frac{Adjacent}{Hypotenuse}[/tex]
This gives:
[tex]\cos(A) = \frac{60}{61}[/tex]
