**Mathematics is a subject that is vital for gaining a better perspective on events that occur in the natural world. **

PentaCalc is capable of calculating the trigonometric functions and their inverses using degrees, radians, or grads. The default mode is degrees. To change the angular mode, make the selection from the Option menu.

**Flagpole Example**

Your company recently erected a new flagpole, and the city engineer has just informed you that it is too high and in violation of city ordinances. He said the maximum height for a flagpole is 75 feet. When you asked him how he knows your flagpole is over 75 feet, he curtly replies, "I know my flagpoles." You are sure it is under 75 feet, but how can you prove it?

Note: If we have offended any city engineers with this example, we apologize.

Solution: This is a simple trigonometry problem. If you know one angle and one side of a right triangle, you can solve for any other angle or side. You know a spot in the parking lot that is exactly 125 feet away from the flagpole. You also have an inclinometer (an instrument with a sighting device used to measure the angle between the horizon and some point above the horizon). A quick check with the inclinometer shows the angle between the spot in the parking lot and the top of the flagpole is 27.5°. You may now use the tangent function to solve the equation: (Tan 27.5°)(125 ft) = the height of the flagpole. Make sure PentaCalc is in degrees mode before calculating this example.

# Q.E.D.

Thus you are able to prove that the flagpole will comply with the ordinance and have 10 feet to spare.