Question

0.32. If the angles of elevation of the top of the candle from two coins
distance a cm and b cm (a>b) from its base and in the same straight line
from it are 30' and 60', then find the height of the candle​

Answer 1

Let AB be the height of the tower and B be its foot

AB=h

BD=b

BC=a

∠ADC=60

o

∠ACB=30

o

In △ABC

tan30=

BC

AB

3

1

=

a

h

h=

3

a

.....(1)

In △ADB

tan60=

b

h

3

=

h

h=b

3

.....(2)

Multiplying (1) and (2)

h

2

=

3

a

×b

3

h

2

=ab

h=

ab