A man views a car from the top of the building at a distance of 6km from him and a bus 8km from him on the same road. From the man the angle subtended by two vehicles is 60°. Find the distance between car and Bus.
Answers
Step-by-step explanation:
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:height of hill = 200m. = AB
let ,the distance between two vehicles {ym}= DC
BD = xm
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
thus, the distance between the vehicles = 230.940m
Step-by-step explanation: