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Question Number 10265 by Tawakalitu ayo mi last updated on 31/Jan/17

From the top of a 100 m high building, a man observes the top of a tree at an angle of depression 30°. If the tree is 50 m tall, the angle of depression of the foot of the tree is viewed by the man is ?

$$\mathrm{From}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{a}\:\mathrm{100}\:\mathrm{m}\:\mathrm{high}\:\mathrm{building},\:\mathrm{a}\:\mathrm{man} \\ $$$$\mathrm{observes}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{a}\:\mathrm{tree}\:\mathrm{at}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of} \\ $$$$\mathrm{depression}\:\mathrm{30}°.\:\mathrm{If}\:\mathrm{the}\:\mathrm{tree}\:\mathrm{is}\:\mathrm{50}\:\mathrm{m}\:\mathrm{tall},\:\mathrm{the} \\ $$$$\mathrm{angle}\:\mathrm{of}\:\mathrm{depression}\:\mathrm{of}\:\mathrm{the}\:\mathrm{foot}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tree}\:\mathrm{is} \\ $$$$\mathrm{viewed}\:\mathrm{by}\:\mathrm{the}\:\mathrm{man}\:\mathrm{is}\:? \\ $$

Answered by sandy_suhendra last updated on 01/Feb/17

Commented by sandy_suhendra last updated on 01/Feb/17

△ABC⇒tan 30°=((BC)/(AB)) AB=((BC)/(tan 30°))=((50)/(0.577))=86.66 m △ABD⇒tan∠BAD=((BD)/(AB))=((100)/(86.66))=1.154 ∠BAD=49° (depression of the foot of the tree)

$$\bigtriangleup\mathrm{ABC}\Rightarrow\mathrm{tan}\:\mathrm{30}°=\frac{\mathrm{BC}}{\mathrm{AB}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{AB}=\frac{\mathrm{BC}}{\mathrm{tan}\:\mathrm{30}°}=\frac{\mathrm{50}}{\mathrm{0}.\mathrm{577}}=\mathrm{86}.\mathrm{66}\:\mathrm{m} \\ $$$$\bigtriangleup\mathrm{ABD}\Rightarrow\mathrm{tan}\angle\mathrm{BAD}=\frac{\mathrm{BD}}{\mathrm{AB}}=\frac{\mathrm{100}}{\mathrm{86}.\mathrm{66}}=\mathrm{1}.\mathrm{154} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\angle\mathrm{BAD}=\mathrm{49}°\:\left(\mathrm{depression}\:\mathrm{of}\:\mathrm{the}\:\mathrm{foot}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tree}\right) \\ $$

Commented by Tawakalitu ayo mi last updated on 01/Feb/17

I really appreciate sir. God bless you.

$$\mathrm{I}\:\mathrm{really}\:\mathrm{appreciate}\:\mathrm{sir}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}. \\ $$

Commented by Tawakalitu ayo mi last updated on 01/Feb/17

please how is BC = 50

$$\mathrm{please}\:\mathrm{how}\:\mathrm{is}\:\mathrm{BC}\:=\:\mathrm{50} \\ $$

Commented by Tawakalitu ayo mi last updated on 01/Feb/17

i got it now sir. BC = 100 − 50 BC = 50 m

$$\mathrm{i}\:\mathrm{got}\:\mathrm{it}\:\mathrm{now}\:\mathrm{sir}. \\ $$$$\mathrm{BC}\:=\:\mathrm{100}\:−\:\mathrm{50} \\ $$$$\mathrm{BC}\:=\:\mathrm{50}\:\mathrm{m} \\ $$

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