In the triangle the length of side a is 5 ft and measurement of angle A =60 degrees measurement of angle B=30 degrees measurement of angle C=90 degrees find the exact lengths of sides b and c
We can use the sine and cosine functions to find the lengths of sides b and c.
First, we can find the length of side b using the sine function:
sin(A) = opposite/hypotenuse
sin(60) = b/5
√3/2 = b/5
b = 5 * √3/2
b = 5√3/2
b = (5√3)/2 ft
Next, we can find the length of side c using the cosine function:
cos(B) = adjacent/hypotenuse
cos(30) = c/5
√3/2 = c/5
c = 5 * √3/2
c = 5√3/2
c = (5√3)/2 ft
Therefore, the exact lengths of sides b and c are (5√3)/2 ft each.