from the top of a building 60 m high the angles of depression of the top and bottom of a vertical lamp post are observed to be 30 degree and 60 degree respectively find

1)the horizontal distance between the building and the lamp post

2)the height of the lamp post (use root 3= 1.732)

Asked by ajayrath7 | 12th Aug, 2019, 11:26: AM

Expert Answer:

CD is the height of the lamp and AB is the height of the building

From the diagram,
tan space 30 degree equals fraction numerator A E over denominator E C end fraction
rightwards double arrow E C equals square root of 3 A E
A n d space tan space 60 degree equals fraction numerator A B over denominator B D end fraction
rightwards double arrow A B equals square root of 3 B D equals square root of 3 E C space.... space left parenthesis E C equals B D right parenthesis
rightwards double arrow E C equals fraction numerator A B over denominator square root of 3 end fraction equals fraction numerator 60 over denominator square root of 3 end fraction equals 20 square root of 3
rightwards double arrow A E equals 20 m
rightwards double arrow E B equals A B minus A E equals 60 minus 20 equals 40 m
T h e r e f o r e comma space h o r i z o n t a l space d i s tan c e space b e t w e e n space t h e space b u i l d i n g space a n d space l a m p space p o s t space i s space B D equals 20 square root of 3 m
H e i g h t space o f space t h e space l a m p space p o s t equals 40 m

Answered by Renu Varma | 12th Aug, 2019, 11:52: AM