SOLUTION: in right triangle ABC, angle C=90, angle A=55, and CA=10. what is the length of AB to the nearest integer.

Algebra ->  Triangles -> SOLUTION: in right triangle ABC, angle C=90, angle A=55, and CA=10. what is the length of AB to the nearest integer.       Log On


   

Question 697592: in right triangle ABC, angle C=90, angle A=55, and CA=10. what is the length of AB to the nearest integer.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Since side CA is adjacent to angle A and side AB is the hypotenuse. The Trig functions that have adjacent and hypotenuse in their ratios are cos and sec. Since our calculators probably do not have a sec button we will use cos:
cos%2855%29+=+10%2Fx where x is the length of side AB
Multiplying each side be x we can eliminate the fraction:
x%2Acos%2855%29+=+10
Dividing each side by cos(55):
x+=+10%2Fcos%2855%29
This is an exact expression for the solution. For a decimal approximation we use our calculators to divide 10 by cos(55):
x+=+10%2F0.57357643635104609610803191282616
x+=+17.434467956210980198376834167244
Rounded to the nearest integer this would be 17.