Section 0.4 - Interactive checkpoints



		The great pyramid of Cheops has a square base with edges that are almost exactly 230 m long. The side faces of the pyramid make an angle of 51.8° with the ground. The apex of the pyramid is directly above the center of the base. Find its height.

This section shows you an example of an interactive checkpoint. We chose a problem that uses mathematics you may be familiar with in case you would like to solve the problem yourself.

In interactive checkpoints, all of the problem-solving elements are initially hidden. You can open any element by clicking [Show] below.

You can check your answer at any time by entering it at the top and pressing [Check] to see if you are right. You will find this is far more efficient than keying all the information into the computer, which provides a good motivation for you to solve the problem yourself. However, if you are stuck, you can always have the computer help you.

In the parts called Variables, Strategy, and Physics principles and equations, the computer will show you the information you need when you ask. In the Physics principles and equations section, we show you the principles and equations you need to solve the problem, as well as some that do not apply directly to the problem.

In the Step-by-step solution, you choose from the equations by clicking on the one you think you need to use. You must enter the correct values in each Step-by-step part of the solution to proceed to the next step.

Diagram [Hide]

Variables [Hide]
Fill in values for the variables. Press the button labeled [Done] to confirm what you have filled in. You can also press [Show] if you are stuck.
Variable	Value
length of edges of base	b = m
angle between pyramid faces and ground	θ = °
length of leg adjacent to angle	l
height of pyramid	h
I think I'm done.	I need help. Show the correct values.

Strategy [Hide]

Find a suitable right triangle.
Use a trigonometric function to relate the sides of the triangle and the given angle.

Physics principles and equations [Hide]

Here is a list of equations that might be applicable to the problem.

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

c² = a² + b²

Step-by-step solution [Hide]
	Here is where you do the work. You will be asked to do calculations, often starting by selecting an equation from the list and entering values. It may take you several steps to solve the problem, using more than one equation. In these types of problems, some steps require you to enter data. This is the only place in the book where entering correct data is required to get to the next step. Better to work it out here than on a test or quiz! And remember, you can always enter your answer at the top to see if you are right.
Find the triangle	See the diagram if you are having trouble visualizing the triangle.
Calculate the leg length	Compute the length of the leg adjacent to the given angle, which is one-half the length of an edge of the base. l = b / 2 l = ( m) / 2 l = m
3	Select an equation relating the legs of the triangle with the given angle. Click on an equation in the list above. If you click on the correct equation, it will appear below.
Substitute variables	For this problem, tan θ = h / l
Find h	h = l tan θ h = (115 m)(tan °) h = m