Question

A man on the roof of a house which is 10 m high observe the angle of elevation of the top of a building as 45* & the angle of depression of the base of the building as 30*. Find the hdight of building and distance between them

Answer 1

The height of building is h = 10√3 ( √3+1 ) /3 and the distance between them is  10√ 3 /3.

Step-by-step explanation:

Tan(45°) = h/x = 1

Therefore h = x   ---(1)

Tan (30°) = 10/x = √ 3

Therefore x = 10/ √ 3

Now put the value of x in equation (1).

h =  10/ √ 3

Height of building =  10 + 10/ √ 3

                              = 10/ √ 3 + 10 / √ 3

                              = 30 + 10√ 3 / 3

                             = 10√3 ( √3+1 ) /3

Distance = x

Distance = 10/ √ 3 = 10√ 3 /3

Thus the height of building is h = 10√3 ( √3+1 ) /3 and the distance between them is  10√ 3 /3.

Also learn more

The dimensions of a building are 30m,20m ,40m. If the wall, floor and roof of this building are to be repaired the contractor ask for rupees 50 per square metre what will be the estimate of the contractor for this work ?

https://brainly.in/question/7544085

Answer 2

The distance between them is $10\sqrt{3}$ units.

The height of the building is $10(1 + \sqrt{3})$ meters.

Step-by-step explanation:

See the diagram attached.

Let AB is the house with height 10 m and the angle of depression from B to the bottom of the building CD is 30°.

Therefore, considering the Δ CAB, the angle of elevation from C to B will be 30°.

Now, $\tan 30^{\circ} = \frac{AB}{CA} = \frac{10}{CA}$

⇒ $CA = \frac{10}{\tan 30^{\circ}} = 10\sqrt{3}$ meters

Therefore, the distance between the house and the building is $10\sqrt{3}$ units. (Answer)

Now, from the right triangle Δ EBD, the angle of elevation from B to D is 45°.

Hence, $\tan 45 ^{\circ} = \frac{ED}{EB} = \frac{ED}{CA} = \frac{ED}{10\sqrt{3}}$

⇒ $ED = 10\sqrt{3}$ meters  

Therefore, height of the building is CD = CE + ED = AB + ED = $10 + 10\sqrt{3} = 10(1 + \sqrt{3})$ meters.

Therefore, the height of the building is $10(1 + \sqrt{3})$ meters. (Answer)