if the altitude of the sun is 45 then the length of shadow of a h metre high tower standing on a plan will be
If you mean that the angle of elevation of the sun is 45°, then ....
then Length/h = tan45°
length = h(1) = h
Teaching
To find the length of the shadow, you can use the concept of similar triangles.
Let's create a diagram to visualize the scenario. Assume there is a tower with a height of "h" meters, and the altitude of the sun is 45 degrees.
TOWER
|
|
|---------> SHADOW
|
|
/|
/ |
/ |
/ |
______
In this diagram, we can see that the tower, the shadow, and the sun's rays form two similar right-angled triangles. The angle of elevation from the top of the tower to the sun is also 45 degrees.
Using the tangent function, we can relate the height of the tower, the length of its shadow, and the angle of elevation:
tan(45) = height of the tower / length of the shadow
tan(45) is equal to 1, so the equation simplifies to:
1 = h / length of the shadow
To find the length of the shadow, we can rearrange the equation:
length of the shadow = h / 1
Therefore, the length of the shadow of a tower with a height of "h" meters, when the altitude of the sun is 45 degrees, will be equal to the height of the tower.
If you mean that the angle of elevation of the sun is 45°, then ....
then Length/h = tan45°
length = h(1) = h
by 2