A right triangle has a side not the hypotenuse that is three

A right triangle has a side (not the hypotenuse) that is three times the short side. The area of the triangle is thirty. The angle theta is adjacent to the short side. Find the hypotenuse and all six trig functions of theta. Be exact. a. csc(theta = b. sin(theta) = c. cos(theta) = d. tan(theta) = e. cos(theta) = f. sec(theta) = g. The hypotenuse =

Solution

Let Base = b = x

Perp. = a = 3x

Area = A = ab/2 = 30

3x^2 = 60 =======> x = 4.5

So, b = 4.5

a = 13.5

Then hypt = c = sqrt(4.5^2 + 13.5^2) = 14.23

csc = c/a = 14.23/13.5 = 1.054

sin = a/c = 13.5/14.23 = 0.95

cos = b/c = 4.5/14.23 = 0.316

tan = a/b = 13.5/4.5 = 3

cot = b/a = 4.5/13.5 = 0.333

sec = c/b = 14.23/4.5 = 3.16