The shadow of a tower,standing on level ground,is found to be 45m longer when sun's altitude is 30⁰than when it was at 60⁰.Find the height of the tower.

i need help

Question

The shadow of a tower,standing on level ground,is found to be
45m longer when sun's altitude is 300 than when it was
at 600 Find the height of the tower
i need help

Mayank Bhardwaj · Accepted Answer

Dear Student! Here is the answer to your query

Let AB be the tower and AC and AD be its shadow when the sun's attitude is 60Â° and 30Â° respectively Then, CD = 45 meters Let h be the height of the tower and AC = x meters In Î”CAB, we have $\tan {60^{\circ} = \frac{AB}{AC}}^{^{}} \Rightarrow \sqrt{3} = \frac{h}{x} \Rightarrow x = \frac{h}{\sqrt{3}} (1)^{}$ In Î”DAB, we have $\tan 30^{\circ} = \frac{AB}{AD} \Rightarrow \frac{1}{\sqrt{3}} = \frac{h}{x + 45}$ Substituting the value of x from equation (1) we get $\frac{1}{\sqrt{3}} = \frac{h}{\frac{h}{\sqrt{3}} + 45} \Rightarrow \frac{h}{\sqrt{3}} + 45 = h \sqrt{3} \Rightarrow h \sqrt{3} - \frac{h}{\sqrt{3}} = 45 \Rightarrow \frac{3 h - h}{\sqrt{3}} = 45 \Rightarrow 2 h = 45 \sqrt{3} \Rightarrow h = \frac{45 \sqrt{3}}{2} m = \frac{45 \times 1 73}{2} m = \frac{77 85}{20} m = 38 9 m (approx)$ Hence the height of the tower is 38 9 meters (approx) Cheers!

The shadow of a tower,standing on level ground,is found to be 45m longer when sun's altitude is 300 than when it was at 600.Find the height of the tower. i need help

The shadow of a tower,standing on level ground,is found to be 45m longer when sun's altitude is 30⁰than when it was at 60⁰.Find the height of the tower.

i need help