Question

from the top of a building 69 m high the angle of elevation and depression of the top and the foot of another building are a and b respectively find the height of the second building​

Answer 1

Answer:

sushmitha

Secondary School Math 5 points

From the top of a building 60m high, the angle of depression of the top and bottom of a vertical lamp post are observed to be 30° and 60° respectively. Find the height of the lamp post and distance between the building and lamp post

Ask for details Follow Report by Gauravjain9327 15.02.2018

Answers

parmesanchilliwack Ambitious

Answer:

The height of the lamp is 45 meters.

Step-by-step explanation:

Let the line segment AB represents the height of the lamp ( where A is the top of the lamp ), ED represents the height of the building,

While C is any point on ED such that CA ║ DB and CA = DB

Thus, by the below diagram,

In triangle ECA,

tan 30^{\circ}=\frac{EC}{CA}

\frac{1}{\sqrt{3}}=\frac{EC}{CA}\implies CA =\sqrt{3} EC

Now, in triangle EDB,

tan 60^{\circ}=\frac{ED}{DB}=\frac{60}{CA}

\implies \sqrt{3}CA = 60\implies CA = \frac{60}{\sqrt{3}}

Thus,

√3 EC = 60 / √3

⇒ 3 EC = 60 ⇒ EC = 20

Since, AB = CD = ED - EC = 60 - 20 = 40 meters,

Hence, the height of the lamp post is 40 meters.