Zaheer, a boy of height 1.5m was watching the entire programme. Initially he observed the top of the flag pole at an angle of elevation 300 . When he moved 10 m towards the flag post the angle of elevation of the top of the flag pole increased to 450. What is the height of the flag pole?

You need to draw a figure. Start by drawing a horizontal segment approximately 10 cm long; that is the ground. Label the left end point A and the right endpoint B. On the right endpoint, B, go up a short 1 cm vertically. That is 1.5 m, the height of Zaheer. Label that point C. Now from that point draw a horizontal line that ends up above point A. Label that point D. Now go back to point C. Draw a segment up to the left at a 30 deg angle with CD. End the segment vertically above point D. Label that point E. That is the top of the flagpole. Draw a vertical segment down from point E through point D ending at point A. Segment AE is the flagpole. Go back to point C. Move 3 cm to the left on segment CD, and draw a point there and label it F. That is where Zaheer moved to. Now connect point F to point E. That is a 45-deg elevation to point E, the top of the flagpole.

m<EFD = 45 deg

m<EFC = 135 deg

m<FEC = 15 deg

m<ECD = 30 deg

We now use the law of sines to find EC

(sin 15)/10 = (sin 135)/EC

EC = 27.32

Because of the 30-60-90 triangle, ED = EC/2

ED = 13.66

Now we add the height of Zaheer to find AE.

13.66 + 1.5 = 15.16

Answer: 15.2 m