Question

The length of the shadow of a tower when
the sun's elevation is 30° exceeds the length
of its shadow when the sun's elevation is
45° by 2x m. Prove that the height of the
tower is xl 13 +1) m.​

Answer 1

Answer:

Height of tower = x(√3+1)

Step-by-step explanation:

Let the height if the tower be (ab) = h m

Let distance (bc) = y m

In traingle ABC :

tan 45°=ab/bc

1 = h/y

y = h

ln traingle ABD

tan 30° = ab/bd

1/√3=h/2x+y

√3h=2x+y

√3h=2x+h

√3h-h=2x

h(√3-1)=2x

h=2x/√3-1

h=2x/√3-1*√3+1/√3+1

h=2x(√3+1)/3-1

h=2x(√3+1)/2

h=x(√3+1)

Height of tower = x(√3+1)