A wire from the top of a TV tower to the ground makes an angle of 52 degrees with the ground and touches the ground 180 feet from the base of the tower. How high is the tower?
a)290 feet
b)230 feet
c)110 feet
d)140 feet
I'm pretty sure we can eliminate c and d because they are less than 180 feet and weknow the tower has to be at least that right? Or is my thinking wrong, Please help!!!!
Why are you guessing? Why not solve the problem and pick the answer?
Draw a diagram so you can see the problem.
tan 52o = height/180.
solve for height.
Hey there! Don't worry, I'm here to help you with a dose of humor!
Well, it seems like you've already eliminated options C and D based on the given information, so that's a good start! Now let's get to the actual solution and determine the height of the tower.
So, we have the angle between the wire and the ground at 52 degrees and the distance from the base of the tower to where the wire touches the ground is 180 feet.
To solve this, we can use the tangent function (tan) of the angle, which is equal to the height of the tower divided by the distance from the base. So, we have:
tan(52°) = height/180
Now, all we have to do is solve for height. You can either use a scientific calculator or an online calculator to find the tangent of 52° and then multiply it by 180. That will give you the height of the tower.
Remember, the correct answer will be in feet. So go ahead, calculate it, and select the answer that matches your result!
I hope that puts a smile on your face and helps you find the right answer!
To solve this problem, you can use trigonometric ratios, specifically the tangent function.
1. Since we are given the angle of 52 degrees and the distance of 180 feet from the base of the tower to where the wire touches the ground, let's first draw a diagram to visualize the problem.
2. Draw a vertical line to represent the tower and a horizontal line to represent the ground. The wire forms an angle of 52 degrees with the ground, so draw a line from the top of the tower to where the wire touches the ground, forming a right triangle.
3. The given information is that the wire touches the ground at a distance of 180 feet from the base of the tower.
4. Now we can use the tangent function (tan) to find the height of the tower.
tan(angle) = opposite/adjacent
In this case, the opposite side is the height of the tower and the adjacent side is the distance from the base of the tower to where the wire touches the ground.
So, tan(52) = height/180.
5. Now, solve the equation for the height. Multiply both sides of the equation by 180:
height = 180 * tan(52).
6. Use a calculator to find the value of tan(52) and multiply it by 180:
height ≈ 290 feet.
Therefore, the height of the tower is approximately 290 feet.
So, the correct answer is a) 290 feet.