Question

a statue 1.46 tall, stands on the top of the pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60 degrees and from the same point, the angle of elevation of the top of the pedestal is 45 degrees. Find the height of the pedestal.​

Answer 1

Step-by-step explanation:

let hight of the pedestal be h meters,and angle of elevation of C and D at a point A on the ground be 60 and 45 respectively.

It also given the hight of statue CD be 1.6 cm.

angle CAB = 60

angle DAB = 45 and CD= 1.6 cm.

In right angle ABD, we have

tan 45= BD/AB

= 1 = h/AB

= AB= h.................(i)

tan 60 = BC/AB

= √3= BD+DC/AB

= √3= h + 1.46/ AB

= AB= h+ 1.46/√3 .........(ii)

comparing(i) and (ii),we get

h = h+1.46/√3

=√3 h= h + 1.46

= h (√3-1)= 1.46

= h=1.46/√3-1 * √3+1/√3+1

= h=1.46[√3+1] / 3-1

= h = 0.73[√3+1]

hence the hight of pedestal

= 0.73 (1.73+1) = 0.73*2.73

= 1.929m = 2m (approx)

hope it helps you.