"Uncovering the Height of a Tower: A Trigonometry Problem Solved"

 "Uncovering the Height of a Tower: A Trigonometry Problem Solved"

Have you ever looked at a tall tower and wondered just how high it is? In this blog post, we'll work through a problem that demonstrates how to use trigonometry to find the height of a tower.

The problem is as follows: A tower stands vertically on the ground. From a point on the ground 20m away from the foot of the tower, the angle of elevation of the top of the tower 60°. What is the height of the tower?

To solve this problem, we'll be using the tangent function. The tangent function allows us to find the ratio of the opposite side to the adjacent side of a right triangle, given the measure of an angle in the triangle. In this case, we're looking for the height of the tower (the opposite side), and we know the distance from the point on the ground to the base of the tower (the adjacent side) is 20m.

The equation we'll use is:

tan(60°) = h/x

where h is the height of the tower and x is the distance from the point on the ground to the base of the tower.

Plugging in the known values:

tan(60°) = h/20m

we can then solve for h by multiplying both sides by 20m:

h = 20m * tan(60°)

Therefore, the height of the tower is approximately 34.64101615137755m.

This problem is a great example of how trigonometry can be used in real-world applications. It demonstrates how the tangent function, when used with known values, can be used to calculate the height of a structure. In this case, we were able to find the height of a tower, but this same method can be applied to other structures such as buildings, bridges, and even mountains.

In conclusion, trigonometry is an important branch of mathematics that helps us understand and solve real-world problems. By understanding the basic concepts, we can use trigonometry to find the height of a tower and many other things.