Question

If the shadow the tower is 100 m long,when the sun's altitude is 45° what is length of the shadow when the sun's altitude is 60°

Answer 1

shadow of tower is 100 m long when angle by sun is 45°, when the height of Tower would be also 100 m high.....
Now since the height of Tower is 100 then at the angle of 60° the value of sin 60 degree would be....
root 3/2 = 100m / shadow
root 3/2 ×100 = shadow of tower
shadow of tower = 50 root 3
if we put root3 as 1.73
then

shadow of tower = 1.73 × 50
= 86.5 m

Answer 2

$\green{\huge{\underline{Hey\: mate\: !}}}$

Let we consider the "h" be the height of tower 100 m long

Now we know that

$tan 45\degree = \frac{AB}{BC}\\ tan 45\degree = \frac{100}{x_1}\\ 1 = \frac{100}{x_1}\\ x_1 = 100 m$

Now we have have another shadow by angle 60°

$tan 60\degree=\frac{AB}{x_1 - x_2} \\\\ \sqrt3 = \frac{ 100} {100 - x_2}\\ \sqrt 3(100-x_2) = 100\\ \sqrt 3 \times 100 -100 = \sqrt 3 x_2\\ 100\times (\frac{\sqrt3 -1}{\sqrt 3})=x_2 \\ x_2 = 42.264 \:m$

$BD = x_1 - x_2 \\\implies 100 - 42.264 \\\implies 57.736\: m$

$\orange{\underline{Answer}}$

$\pink{\boxed{BD \implies 57.736\: m }}$

$\pink{\boxed{BC = x_1 \implies 100\: m }}$