# FE Exam Practice Problems – Sample #1

Solving practice problems is the most effective way to learn the concepts of engineering subjects. Since you will be facing various topics when you take the exam, it is important to go over plenty of FE exam practice problems.

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This sample problem is from Michael Lindeburg's "FE Civil Review Manual". I know that this has been already solved on the textbook but I just want to show another approach to find the answer to the problem.

### Sample Problem #1 - Mathematics

The vertical angle to the top of a flagpole from point A on the ground is observed to be 37°11’. The observer walks 17 m directly away from the flagpole from point A to point B and finds the new angle to be 25°43’. What is the approximate height of the flagpole?

(a) 10 m

(b) 22 m

(c) 82 m

(d) 300 m

Like any other problem, you should first write down the given. If possible create a sketch to better understand the question.

There are three values given in the problem. The angle at B is 25°43’, angle at A is 37°11’ and the distance from A to B is 17m. Set h = height of flagpole. Set x = distance from A to D.

The required on the problem is the height of the flagpole.

Convert the angle to its decimal form. This would help you when plugging in the numbers on the calculator. Also, always bring the value to 4 significant figures. This will ensure that you will get the closest possible answer.

Example, 25°43’ has a decimal form of 25.716667 and becomes 25.72 if we consider 4 significant figures.

Come up with equations to correlate all the given on the problem. If we use the tangent formula, tan θ = y / x , we will arrive with equation number 1 and 2.

Simplify equation number 2 and you will get the value of h in terms of x.

Solve for x using equation number 1. Just do the basic algebra. After that, substitute the value of h. This will help you arrive to a numeric value of x. So the distance from A to D will be 29.58 m.

The next step is to substitute the value of x to equation number 2. This will give the value of h which is 22.44 m. Among the choices, the closest answer would be letter (b) 22 m. So the approximate height of the flagpole is 22 m.

For your reference, you will see below the complete solution to this sample problem.

The only reason that I showed this solution is to share to you that there are plenty of ways to arrive to the correct answer. There are a lot of approaches that you can use to find the required on the problem. It is just a matter of personal preference.

If ever you have a specific problem that you want me to go over or find the required answer, just write it down in the comment box below and I will try to solve it at the soonest possible time.

##### John Rico

John Rico is an Engineer-in-Training Professional that works his way up to become a Licensed Professional Engineer.

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