How do mechanical engineers use trigonometry

Structural engineers can also map light and sound patterns through a room using expressions from trigonometry. Electrical engineers design and test electrical layouts, mapping out requirements and flows of electricity throughout a building.

Almost any type of engineer is able to combine their knowledge of trigonometry with computer expertise to create or debug computer programs to simulate and design things in their respective fields. Where might engineers use trigonometry?

For what types of projects might engineers use clinometers? When finished, summarize students' results on the classroom board so that the entire class benefits from student research on how engineers use trigonometry and the possible engineering applications of trigonometry and clinometer use. Similar triangles are the basis for right-triangle trigonometry.

Since right angles are congruent, any right triangles that have one other corresponding angle congruent will be similar by geometry's angle-angle similarity postulate. When triangles are similar, the ratios of corresponding sides will be equal. Trigonometry uses this property of similar triangles by calculating the ratios of two sides in a triangle.

For instance, sine is the ratio of the side opposite the angle to the hypotenuse in a right triangle. A clinometer is a device that can be used to measure angles. The app on a mobile device allows you to use the mobile device to measure angles.

By placing the device on a sloped surface and using the clinometer app, the angle of the sloped surface can be read. Clinometers can be used to measure angles between objects or the tilt of a stationary object, allowing for indirect measurement of distance using trigonometry.

The Android or iOS device must be nearly vertical to use the angle measuring function of the clinometer, when it is in the mode matching that of Figure 3. The degree measure of the angle can then be read from the clinometer.

Figure 4 shows the alignment of the clinometer in measuring an angle. Figure 4. Measuring an angle with the clinometer app. Civil engineers often need to measure very large objects, such as skyscrapers and bridges. It is impractical, and often impossible, to measure these objects with a tape measure.

When direct measurements are not possible, technology and mathematics are used instead. Right-triangle trigonometry uses one side of a triangle that is known, combined with a known angle to calculate the other sides of the triangle which might be the height or length of a building, for example.

Engineers use devices such as clinometers to measure the angle required to perform trigonometric calculations. Trig functions are ratios of the legs and hypotenuse of the right triangles used in the Pythagorean Theorem. The basic trig functions are related to the reference angle the given angle or its equivalent. Figure 5. A right triangle in a circle on a coordinate plane. Figure 5 shows a right triangle placed on a coordinate plane with one of its vertices on the origin of the coordinate plane and the center of a circle.

One side of the triangle is in the x-direction, begins at the origin and extends a length x. The other side of the triangle is in the y-direction, and extends from the point x,0 to x,y. The hypotenuse is of length r and extends from 0,0 to x,y. Begin taking measurements and calculating the dimensions of what you intend to build or create. For example, when studying civil engineering you will have to calculate the force distribution for different structures, such as truss bridges. The engineer must also figure out what the angles between the beams in a bridge must be, and how long they must be.

Build your structure or system according the the measurements. You should also create a specification sheet for your design for future reference. Validate the structural integrity of your work. Does it meet all of your initial requirements?

Is it safe? Have you had it inspected? Computer programming is also about creating something that corresponds to the real world in some way. Math is often the bridge that makes that connection. If a software program matches the math for how many patients a doctor can see in a day and the math matches or at least approaches the real number a given doctor is able to help, that program can be useful for projecting staffing needs at a hospital given a little more data and math about how likely people are to need a doctor in a given area, time of year, weather, or whatever else might affect peoples health or cause accidents or violence.

When coding, most people match the mathematical model because it allows prediction of or application to future situations. No one may ever fire a cannon from the top of Olympus Mons, but we can use math especially trig to predict what would happen if they did with a lot of confidence. Computer programming inherits all of its predictive power and usefulness from math, used repeatedly.

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