Find the value of x sin1x cos145 Solve the triangle a A 74

Find the value of x: sin^-1(x) = cos^-1(4/5) Solve the triangle: a. A = 74.3 degree, b = 151.8 meters, C = 87.2 degree b. A = 44.9 degree, b = 11.42 inches, C = 5.66 inches

Solution

4. sin^-1x = cos^-1(4/5)

taking sine on both sides

x= sin(cos^-1(4/5))

Let cos^-1(4/5) = t

cos t= 4/5

Here adjacent=4     and    hypotenuse=5

Opposite= sqrt(5²-4²) = 3

Sin t= opposite/hypotenuse = 3/5

THerefore sin(cos^-1(4/5)) = 3/5

Hence x=3/5