Solving Right Triangles Word Problems

Solving Right Triangles Word Problems-43
The kite is directly above Ben, who is standing 50 feet away.

The kite is directly above Ben, who is standing 50 feet away.

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In this example, θ represents the angle of elevation.

A wheelchair ramp is placed over a set of stairs so that one end is 2 feet off the ground.

You want to find the measure of an angle that gives you a certain tangent value.

This means that you need to find the inverse tangent.

However, you really only need to know the value of one trigonometric ratio to find the value of any other trigonometric ratio for the same the opposite side to the adjacent side.

The simplest triangle you can use that has that ratio is shown.Finding an angle will usually involve using an inverse trigonometric function.The Greek letter theta, θ, is commonly used to represent an unknown angle. Remember that the two acute angles will give you different trigonometric function values.Use the Pythagorean Theorem to find the opposite side length. The correct answer is Some problems may provide you with the values of two trigonometric ratios for one angle and ask you to find the value of other ratios.Let’s look at how to do this when you’re given one side length and one acute angle measure.Once you learn how to solve a right triangle, you’ll be able to solve many real world applications – such as the ramp problem at the beginning of this lesson – and the only tools you’ll need are the definitions of the trigonometric functions, the Pythagorean Theorem, and a calculator. Substitute the measure of the angle on the left side of the equation and use the triangle to set up the ratio on the right.Remember that you have to use the keys 2ND and TAN on your calculator.Look at the hundredths place to round to the nearest tenth. You may have been confused as to which ratio corresponds to which trigonometric function.The other end is at a point that is a horizontal distance of 28 feet away, as shown in the diagram.What is the angle of elevation to the nearest tenth of a degree?

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