From a window (9m above ground) of a house in a street, the angles of elevation and depression of
the top and foot of another house on the opposite side of the street are 300 and 600 respectively.
Find the height of the opposite house and width of the street.
Answers
Answer:
height of the opposite house is 12 m and width of the street is 3√3 m.
Step-by-step explanation:
Hi,
Let AD be the height at which window is situated,
Given AD = 9
Let the height of the opposite house be BC,
AB the width of the street.
Given the angles of elevation and depression of the top and foot of the street are 30° and 60°
⇒ ∠MDB = 60°
=∠ABD = 60°, since ∠ABD = ∠MDB(Angle of elevation)
ALso, ∠CDM = 30°(Angle of depression)
From triangle ABD, tan ∠ABD = AD/AB
⇒ tan 60° = 9/AB
⇒ AB = 9/√3 = 3√3,
Hence, width of the street = 3√3 m.
From triangle CDM, tan ∠CDM = CM/DM
But DM = AB which is = 3√3
tan 30° = CM/3√3
⇒CM = 3√3*1/√3 = 3 m
Hence, height of the house = BM + MC
= AD + MC
= 9 + 3
=12 m
Hence, the height of the house is 12 m.
Hope, it helped !
height of the opposite house is 12 m and width of the street is 3√3 m.
Let AD be the height at which window is situated,
Given AD = 9
Let the height of the opposite house be BC,
AB the width of the street.
Given the angles of elevation and depression of the top and foot of the street are 30° and 60°
⇒ ∠MDB = 60°
=∠ABD = 60°, since ∠ABD = ∠MDB(Angle of elevation)
ALso, ∠CDM = 30°(Angle of depression)
From triangle ABD, tan ∠ABD = AD/AB
⇒ tan 60° = 9/AB
⇒ AB = 9/√3 = 3√3,
Hence, width of the street = 3√3 m.
From triangle CDM, tan ∠CDM = CM/DM
But DM = AB which is = 3√3
tan 30° = CM/3√3
⇒CM = 3√3*1/√3 = 3 m
Hence, height of the house = BM + MC
= AD + MC
= 9 + 3
=12 m
Hence, the height of the house is 12 m.