Question

A statue1.46 metre tall stands on the top of pedestal.from a point on the ground the angle of elevation of top of statue is 60.and from the same point the angle of elevation of top of pedestal is 45. Find the height of the pedestal

Answer 1

Define x:

Let the height of the pedestal be x

Find the distance between the point of the ground and the foot of the pedestal in term of x:

tan(ø) = opp/distance

tan(45) = x/distance

Distance = x/tan(45)

Distance = x

Find the height of the pedestal:

tan(ø) = opp/distance

tan(60) = (x + 1.46)/x

x tan(60) = x + 1.46

x tan(60)  - x = 1.46

x(tan(60) - 1) = 1.46

x = 1.46 ÷ (tan(60) - 1) = 1.99 m

Answer: The height of the pedestal is 1.99 m

Answer 2

tan 45 degree = P/B
1= h/x
h=x. (1equation)
tan60 degree= h+1.46/x
xsqrt3 =h+1.46
h sqrt3-h = 1.46. (h = x)

h( sqrt3-1) =1.46
h = 1.46/(sqrt3-1)
h=1.46 ( sqrt3+1)/2

h=73 (sqrt3+1) cm