Question

In the given diagram, AB is a vertical tower 100 m away from the foot of a 30 storied building CD. The angles of depression from the point C and E, (E being the mid-point of CD), are 35° and 14° respectively.

(Use a mathematical table for the required values rounded off correct to two places of decimals only)

Find the height of the:

1. tower AB
2. building CD

Answer 1

(a) In ΔCAP,

tan 35° = `"CP"/"AP"`

tan 35° = `"CP"/100`    ...[∴ AP = BD = 100 m] 

0.70 × 100 = CP    ... [∴ tan 35° = 0.70]

CP = 70 m

In ΔEAP,

tan 14° = `(EP)/(AP)`

tan 14° = `(EP)/100`

0.25 × 100 = EP

EP = 25 m

СЕ = CP – ЕP

= 70 – 25

= 45m

Since E is the midpoint of CD

CE = DE

DE = 45m

PD = DE − EP

= 45 − 25

= 20m

∴ AB = PD = 20m

(b) Building CD = CE + DE

= 45 + 45

= 90 m