Question

The angle of elevation of the top of a tree from a point 60m from its base is 30°. What will be the
angle of elevation if the observer moves 40m nearer to the tree?
​

Answer 1

Answer:

27.3

Step-by-step explanation:

Let AB be the tower and C and D be the point of observation

Given CD =20 m And ∠BCA=30

0

and ∠BDA=30+15=45

0

Let height of tower is h

In triangle BAD

tan45

0

=

AD

AB

⇒1=

AD

h

⇒AD=h

In triangle BAC

tan30

0

=

AC

AB

( AC=CD+AD)

⇒

3

1

=

20+h

h

⇒

3

h=20+h⇒

3

h−h=20

⇒h(1.732−1)=20

⇒h=

0.732

20

=27.3