Question

ton and the bottom of a 7 m tall building from the top of a
The angles of depression of the top and the bottom of a
tower are 45 and 60", respectively. Find the height of the tower.​

Answer 1

Answer:

In ΔAEC\Delta AECΔAEC

AECE=tan⁡45∘\frac{AE}{CE}=\tan 45^{\circ}CEAE​=tan45∘

AE=CEAE=CEAE=CE  -----  (i)

In ΔABD\Delta ABDΔABD

ABBD=tan⁡60∘\frac{AB}{BD}=\tan 60^{\circ}BDAB​=tan60∘

AE+EBBD=3\frac{AE+EB}{BD}=\sqrt3BDAE+EB​=3

​

AE+7CE=3\frac{AE+7}{CE}=\sqrt3CEAE+7​=3

​

AE+7AE=3\frac{AE+7}{AE}=\sqrt3AEAE+7​=3

​   ---  from (i)

AE=73−1AE=\frac{7}{\sqrt3-1}AE=3

​−17​

So, height of the tower =AB=AB=AB

=73−1+7=\frac{7}{\sqrt3-1}+7=3

​−17​+7

=72(3+3)  m=\frac{7}{2}(3+\sqrt3) \;m=27​(3+3

​)m

Step-by-step explanation: