When the angle of elevation of the sin55 a tower cast a shadow 20m long. Find the height of the tower
20sin55 is equal to 16.4 m
The wording is a bit murky. I think you meant to say
When the angle of elevation of the sun is 55°
Given that, however, the height h is given by
h/20 = tan 55°
To find the height of the tower, we can use trigonometry. In this case, the angle of elevation is given as 55 degrees, and the length of the shadow is given as 20 meters.
Let's break down the problem into two parts: the opposite side and the adjacent side of the angle.
1. Opposite side (height of the tower):
The opposite side is the height of the tower, which is what we want to find. Let's represent it as 'h'.
2. Adjacent side (length of the shadow):
The adjacent side is the length of the shadow, which is given as 20 meters.
Now, we can use the trigonometric function 'tangent' (tan) to relate the opposite and adjacent sides of the right triangle. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
In this case, we have:
tan(angle) = opposite/adjacent
tan(55) = h/20
To find the height of the tower (h), we can rearrange the equation:
h = tan(55) * 20
You can now calculate the height of the tower using a scientific calculator or built-in trigonometric functions on your computer or smartphone.