At a point on the ground 30 feet from the base of a tower, the distance to the top of the tower is 2 feet more than twice the height of the tower. Find the height of the tower.
√(h^2+30^2) = 2h+2
Looks like h=16
pretty puny tower...
To solve this problem, let's break it down step by step:
Step 1: Assign variables
Let's assign variables to the unknown quantities in the problem.
Let:
- "x" be the height of the tower (in feet).
Step 2: Set up the equation
According to the problem, at a point on the ground 30 feet from the base of the tower, the distance to the top of the tower is 2 feet more than twice the height of the tower. This can be expressed mathematically as:
x + 2 = 2x + 30
Step 3: Solve for x
Now, we can solve the equation for x.
x + 2 = 2x + 30
First, let's simplify the equation by combining like terms:
x - 2x = 30 - 2
Simplifying further:
-x = 28
To get rid of the negative sign, multiply both sides of the equation by -1:
x = -28
Since the height of a tower cannot be negative, we know that there must be an error in our calculations or assumptions. Let's go back to Step 2 and review the problem statement.
Upon reviewing the problem statement, it seems we made a mistake. It states that "the distance to the top of the tower is 2 feet more than twice the height of the tower." This means the equation should be:
x + 30 = 2x + 2
Let's proceed with the correct equation:
Step 2: Set up the equation (revised)
x + 30 = 2x + 2
Step 3: Solve for x (revised)
Now, we can solve the revised equation for x.
x + 30 = 2x + 2
First, let's simplify the equation by combining like terms:
x - 2x = 2 - 30
Simplifying further:
-x = -28
To get rid of the negative sign, multiply both sides of the equation by -1:
x = 28
Therefore, the height of the tower is 28 feet.