Ok so I have this word problem that I can't figure out. Help please!!
Sandra is trying to use her old cell phone to call her best friend. She can be no more than 3 miles from a tower in order to get a signal for her phone. If the telephone tower is 252 feet tall, find the angle of elevation, m, when Sandra's phone is the maximum 3 miles from the tower.
THE BASKETBALL TEAM ORDERED TWO PIZZAS. THEY LEFT1/3 OF ONE AND1/4 OF THE OTHER. HOW MUCH PIZZA WAS LEFT!
To find the angle of elevation, we can use trigonometry. Specifically, we can use the tangent function.
First, let's convert the height of the tower to the same unit as the distance. Since 1 mile is equal to 5280 feet, the height of the tower in miles is 252/5280 = 0.0477 miles.
Now we can set up a right triangle to represent the situation. Let's assume that the height of the tower is the opposite side and the distance from Sandra's phone to the tower is the adjacent side.
Let's use "x" to represent the angle of elevation.
We know that the tangent of an angle is equal to the opposite side divided by the adjacent side:
tan(x) = opposite/adjacent
Plugging in the values, we have:
tan(x) = 0.0477/3
Now, to solve for x, we can take the inverse tangent (also known as arctangent) of both sides of the equation:
x = arctan(0.0477/3)
Using a calculator, we find that x is approximately 0.948 degrees (rounded to three decimal places).
Therefore, the angle of elevation, m, when Sandra's phone is the maximum 3 miles from the tower is approximately 0.948 degrees.
To find the angle of elevation, we first need to understand the concept of tangent, which relates the angle of elevation to the height and distance.
In this case, the height of the tower is 252 feet. Let's label this as the opposite side (o) of our right triangle. The distance from the tower to the phone is 3 miles, which is equivalent to 3,168 feet. This distance can be considered as the adjacent side (a) of the triangle.
Now, we can use the tangent function. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side:
tan(m) = o / a
Substituting the given values, we get:
tan(m) = 252 / 3168
To find the angle of elevation (m), we need to take the inverse tangent (also known as arctangent) of both sides:
m = arctan(252 / 3168)
Plugging this into a calculator will give you the value of m. Remember to set your calculator to degrees or radians, depending on what is required in the problem.
So, to find the angle of elevation (m) when Sandra's phone is 3 miles from the tower, you can evaluate arctan(252 / 3168) using a calculator.