Question

There is a 10 m tall building just beside a lake. A girl standing on
the top of the building finds that the angle of elevation of a cloud
is 30º and the angle of depression of its image in the lake is 60º.
What is the height of the cloud above the ground?​

Answer 1

Answer:

13.33m

Step-by-step explanation:

Part 1(lake)

height of building = 10m (perpendicular to horizontal line i.e., the base)

angle l= 60 degrees

tan l = tan 60

perp/base=root 3

base= perp/root3

=10m/root3

Part 2(cloud)

height of cloud= perpendicular (to the horizontal line,i.e. , the base)

angle c=30

tan c = tan 30

perp/base = 1/root 3

perp = (1/root 3) x base

=( 1/root 3) x (10m/root 3)

= 10m/3m

=3.333333.......m

=3.33m

Final part

height of cloud above ground = total height

= 10m + 3.33m

= 13.33m