How do I set up this question to solve it

Question

A fire truck has a 75-foot ladder. If the truck is parked 20 feet from a building,how far up the building can the ladder reach assuming that the top of the base of the ladder is resting on the top of the truck and the truck is 10 ft tall?

Answer 1

Hello, Rebecca,

Here is what you know:  distance from base of ladder to building=20 feet,  building's total height= 10ft +x   

      

      || \

x     |   \75ft ladder leaning against building

      |     \

      |__   \_ ___truck_____

10  |   20    O              O

 

It will work nicely if you find "x,"and then add that amount to 10 feet, which is from the base of the building up to where "x" starts.  Use the Pythagorean Equation: a² +b²=c²

 

x² + 20² =(75)²            x² + 400 =5,625             Solve for "x" by first isolating "x^2." 

 

 

Do this by subtracting 400 from both sides of the equation.                              

                                                                                                                      ____

To solve for "x,"  You will need to square root both sides of the equation.  Note:  √x^{2         =} x  because x*x= x2

 

When you find the value of "x," then just add the 10 ft. to find the total distance from the ground to the top of the ladder.

I will let you finish your problem.    Susan C.

 

 

Answer 2

You have a right triangle with two sides, so you just use the Pythagorean Theorem to find the third side.  Since the 75-foot ladder is leaning, it is the hypotenuse.  Since the truck is 20 feet from the building, that's your base.  The third side is the height, but remember the base is 10 feet off the ground, so the actual height is the length of the third side plus 10 feet.