Two buildings in a plane are 20m apart. From the top of smaller building one sees the base of other at a depression of 50°and its top at an elevation 25°. Find the height of the buildings?
Answers
height of buildings 38.2 m and 47.52 m .
let height of smaller building is h and height of bigger building is (h + x).
see figure, here it is given that two buildings of heights h and (h + x) in a plane are 20m apart. From the top of smaller building one sees the base of other at a depression of 50°and its top at an elevation 25°.
from figure, tan50° = h/20
⇒h = 20tan50° ......(1)
and tan25° = x/20
⇒x = 20tan25° .........(2)
height smaller building = h = 20tan50°
[as tan50° = 1.91 and tan25° = 0.466 ]
so, height of smaller building = 20(1.91) = 38.2 m
and height of bigger building = h + x
= 20tan50° + 20tan25°
= 20(1.91) + 20(0.466)
= 38.2 m + 9.32 m
= 47.52 m
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Answer:
Step-by-step explanation:
ABC is a triangle