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

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

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

Answered by sandy_suhendra last updated on 01/Feb/17

Commented by sandy_suhendra last updated on 01/Feb/17

$$△\mathrm{ABC}\Rightarrow \tan 30°=\frac{\mathrm{BC}}{\mathrm{AB}}$$$$\mathrm{AB}=\frac{\mathrm{BC}}{\tan 30°}=\frac{50}{0.577}=86.66\mathrm{m}$$$$△\mathrm{ABD}\Rightarrow \tan \mathrm{\angle }\mathrm{BAD}=\frac{\mathrm{BD}}{\mathrm{AB}}=\frac{100}{86.66}=1.154$$$$\mathrm{\angle }\mathrm{BAD}=49°\left(\mathrm{depression}\mathrm{of}\mathrm{the}\mathrm{foot}\mathrm{of}\mathrm{the}\mathrm{tree}\right)$$

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

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

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

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

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

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

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