The angles of Depression of the top and the Bottom of an 8m tall Building from the top of a multi-storeyed Building are 30°and 45°,respectively. Find the height of the multi - storeyed building
and the Distance between the two buildings
and the Distance between the two buildings
Answers & Comments
Answer:
Height of the Multi-storyed building = AC = 4(3 + √3)m
Distance between 2 buildings = BE (or) CD = 4(3 + √3)m
Step-by-step explanation:
Hope you're preparing for CBSE grade 10 math board exam well because this question is what I exactly solved yesterday
I will attach you the rough diagram so refer that
From the diagram, we can say ED is 8m
In Triangle ACD,
tan45° = AC/CD
1 = AC/CD
CD = AC -> 1
BE = CD (They are the distance between two buildings)
In triangle ABE
tan30° = AB/BE
1/√3 = AC-8/BE
BE = (AC-8) √3 -> 2
Equating 1 and 2 as BE = CD,
(AC-8)√3 = AC
√3AC - 8√3 = AC
8√3 = √3AC - AC
8√3 = AC(√3 - 1)
AC = 8√3/(√3 - 1)
Rationalizing the denominator we get,
(24 + 8√3)/2 = AC
12 + 4√3 = AC
4(3+√3) = AC
Height of the Multi-storyed building = AC = 4(3 + √3)m
Distance between 2 buildings = BE (or) CD = 4(3 + √3)m
Brainliest plsss