Question

The angles of elevation froma point X to the top of flagpoles A and B are 35* and 45* respectively. If X lies in the middle of the flagpoles, find the ratio of the heights of the two flagpoles. Give your answer as a decimal, correct to 1 decimal place.

Answer 1

Let AB = t. And since X lies in the middle, so AX=BX = t/2 .

Let the height of the smaller flagpole is AO and of larger flagpole is BP .

Using tangent ratio rule in each triangle, we will get

$tan 35 =\frac{AO}{t/2} , tan 45= \frac{BP}{t/2} // AO = \frac{t*tan35}{2}, BP=\frac{t*tan45}{2}$

And there ratio is

$\frac{AO}{BP}= \frac{tan 35}{tan 45}=\frac{0.7}{1}$