The top of a T.V tower casts a shadow of 35 metres long when the angle of elevation of the sun 57°40'.How high is the top of the tower?

hi from cherie

h/35 = tan 57°40'

To find the height of the top of the tower, we can use trigonometry. We will need to break down the information given.

We are given the length of the shadow (35 meters) and the angle of elevation of the sun (57°40'). Let's call the height of the top of the tower "h."

We can set up a right triangle with the tower's height as the opposite side and the length of the shadow as the adjacent side. The angle of elevation will be the angle opposite the height of the tower.

Using the trigonometric function tangent (tan), we can relate the angle of elevation to the height and the length of the shadow:

tan(angle) = opposite / adjacent

tan(57°40') = h / 35

To solve for h, isolate it by multiplying both sides of the equation by 35:

h = 35 * tan(57°40')

Now we can calculate the height of the top of the tower:

h ≈ 35 * tan(57°40')

Using a scientific calculator, we find that:

h ≈ 35 * 1.5406

h ≈ 54.12 meters

So, the height of the top of the tower is approximately 54.12 meters.