A vertical tower subtends a right angle on the top of 10m high flagstaff if distance between them is 20m,find - Maths - Some Applications of Trigonometry

Question

A vertical tower subtends a right angle on the top of 10m high
flagstaff if distance between them is 20m,find the height of the
tower! ans given is 50m but i am not able 2 draw a figure n i have
understood it ! plz help!

Gursheen kaur. · Accepted Answer

In Î”BAD, Using Pythagoras theorem, ${(A B)}^{2} + {(D A)}^{2} = {(D B)}^{2} \Rightarrow {(20)}^{2} + {(10)}^{2} = {(D B)}^{2} \Rightarrow 400 + 100 = {(D B)}^{2} o r \Rightarrow D B = \sqrt{500} \Rightarrow D B = 10 \sqrt{5} m I n Δ A B D, \tan θ = \frac{p e r p}{b a s e} = \frac{1}{2} ∴ \sin θ = \frac{1}{\sqrt{5}}$ In Î”BDC, $\cos (90^{0} - θ) = \frac{b a s e}{h y p o} \Rightarrow \sin θ = \frac{10 \sqrt{5}}{h} \Rightarrow \frac{1}{\sqrt{5}} = \frac{10 \sqrt{5}}{h} \Rightarrow h = 10 \sqrt{5} \times \sqrt{5} = 10 \times 5 \Rightarrow h = 50 m$

A vertical tower subtends a right angle on the top of 10m high flagstaff.if distance between them is 20m,find the height of the tower! ans given is 50m...but i am not able 2 draw a figure n i have understood it ! plz help!