Question

If the angle of elevation of the top of a tower of height h meters from a point A in the plane of
ne base of the tower is 30°, then the distance of the base of the tower from A is.....(20 points)

Answer 1

Answer:

ANSWER

Let AB be the tower and let C and D be the two points of the observer. Then,

AC = a metres and AD = b metres

Let ∠ACB=θ. Then, ∠ADB=(90

o

−θ).

Let AB = h metres

In right △CAB, we have

tanθ=

AD

AB

tanθ=

a

h

h=atanθ ......(1)

In right △DAB, we have,

tan(90

o

−θ)=

AD

AB

cotθ=

b

h

h=bcotθ .......(2)

From 1 and 2, we get,

h

2

=ab

h=

ab

metres

solution