Question

As observed from the top of a hill 200 m high, the angles of depression of two vehicles situated on the same side of the hill are found to have measure 30 and 60 respectively. Find the distance between the two vehicles.

Answer 1

HELLO DEAR,

GIVEN:-

height of hill = 200m. = AB

let the distance between two vehicles = ym. = DC

BD = xm

[ figure is in the attachment ]

IN ∆ ABD ,

tan60° = AB/BD

⇒√3 = 200/x

⇒x = 200/√3--------( 1 )

IN ∆ ABC ,

tan30° = AB/BC

⇒1/√3 = 200/(BD + DC) [ ∴BC = BD + DC]

⇒1/√3 = 200/(x + y) [ ∴BD = x , DC = y]

⇒x + y = 200√3 [ ∴x = 200/√3]

⇒200/√3 + y = 200√3

⇒y = 200√3 - 200/√3

⇒y = (200*3 - 200)/√3

⇒y = (600 - 200)/√3

⇒y = (400)/√3

⇒y = 230.940m

Hence, the distance between the vehicles = 230.940m

I HOPE ITS HELP YOU DEAR,

THANKS

Answer 2

Answer:

Step-by-step explanation:

Hope this will help you