The top of a T .V .tower casts a shadow 35 metres long when the angle of elevation of the sun 57 degree40 minutes.How high is the top of the tower?
tan57.67 = Y/X = Y/35.
Solve for Y.
To find the height of the top of the TV tower, we can use the concept of trigonometry.
First, let's understand the given information. We know that the shadow cast by the TV tower is 35 meters long. We are also given the angle of elevation of the sun, which is 57 degrees 40 minutes.
Now, let's define some terms. Let 'h' represent the height of the TV tower.
Using trigonometry, we can define the tangent function:
tan(angle) = opposite / adjacent
In this case, the angle is the angle of elevation of the sun, the opposite side is the height of the TV tower (h), and the adjacent side is the length of the shadow (35 meters).
Therefore, we can set up the equation as:
tan(57 degrees 40 minutes) = h / 35
Before we proceed, we need to convert the angle in degrees and minutes to decimal form. To do this, we divide the minutes by 60 and add it to the degrees:
57 + (40 / 60) = 57.67 degrees
Now, our equation becomes:
tan(57.67 degrees) = h / 35
We can solve this equation to find the value of h. By rearranging the equation, we get:
h = tan(57.67 degrees) * 35
Using a scientific calculator, we can find the value of tan(57.67 degrees) and multiply it by 35 to get the value of h.
Plugging the values into a calculator, we find:
h ≈ 60.03 meters
Therefore, the top of the TV tower is approximately 60.03 meters high.