Given triangle ABC with angle B equal to 90 degrees AB 8 an

Given triangle ABC with angle B equal to 90 degrees, AB = 8 and BC = 12, find the measures of all six trig functions for angle A and angle C. Place the degree angle measure of each angle in the dashed blanks inside the circle, and the radian measure of each angle in the solid blanks inside the circle. Place the coordinates of each point in the ordered pain outside the circle.

Solution

Solution:

Given B = 90° , AB = 8, BC = 12

here AB is Base, BC is height and AC is hypotenuse of triangle.

By Pythogoras theorem;

AC^2 = AB^2 + BC^2

AC^2 = 8^2 + 12^2 = 208

AC = 413

By property;

a/sinA = b/sinB = c/sinB

here a = BC, b = AC and c = AB

12/SinA = 413/Sin90°

=>12/SinA = 413

=> SinA = 3/13

And

413/Sin90° = 8/SinC

=> 413 = 8/SinC

=> SinC = 8/(413) = 2/13

So

SinA = 3/13

CosA = Sqrt(1 - sin^2(A)) = Sqrt(1 - (3/13)^2) = 2/13

tanA = SinA/cosA = (3/13) / (2/13) = 3/2

cot A = 1/tanA = 1/(3/2) = 2/3

secA = 1/cosA = 1/(2/13) = (13)/2

cscA = 1/sinA = 1/(3/13) = (13)/3

and

SinC = 2/13

CosC = Sqrt(1 - sin^2(C)) = Sqrt(1 - (2/13)^2) = 3/13

tanC = SinC/cosC = (2/13) / (3/13) = 2/3

cot C = 1/tanC = 1/(2/3) = 3/2

secC = 1/cosC = 1/(3/13) = (13)/3

cscC = 1/sinC = 1/(2/13) = (13)/2