A wire from the top of a TV tower makes an angle of 49.5 with the ground and touches the ground 225 feet from the base of the tower. How high is the tower?
263.44 ft.
h/225= tangent 49.5deg If I understand the picture correctly, check me.
solve for h.
146.13 feet
To find the height of the tower, we can use trigonometry. Let's call the height of the tower h.
First, we can visualize the situation. Imagine a right-angled triangle with the TV tower as the vertical side, the wire as the hypotenuse, and the distance from the base of the tower to the point where the wire touches the ground as the base of the triangle.
Given that the wire makes an angle of 49.5 degrees with the ground, we can consider the following trigonometric relationship:
sin(angle) = opposite/hypotenuse
In this case, the opposite side is the height of the tower (h), and the hypotenuse is the length of the wire. We need to find h.
We are given that the wire touches the ground 225 feet from the base of the tower. Therefore, the base (adjacent side) of the triangle is 225 feet.
Now, rearranging the trigonometric equation, we have:
sin(49.5) = h/225
To find h, we can multiply both sides of the equation by 225:
225 * sin(49.5) = h
Using a calculator, we can evaluate the expression:
h ≈ 169.6 feet
Therefore, the height of the TV tower is approximately 169.6 feet.