Solving Right Triangles Word Problems

To find c (the length of the hypotenuse), we can use the sine function because we know that and we know the length of the opposite side There are situations in the real world, such as building a ramp for a loading dock, in which you have a right triangle with certain information about the sides and angles, and you wish to find unknown measures of sides or angles.This is where understanding trigonometry can help you. Emma can see that the kite string she is holding is making a 70° angle with the ground.

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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.

If you split the equilateral triangle down the middle, you produce two triangles with 30°, 60° and 90° angles. They both have a hypotenuse of length 2 and a base of length 1.

You can use this triangle (which is sometimes called a 30° - 60° - 90° triangle) to find all of the trigonometric functions for 30° and 60°.

The simplest triangle we can use that has that ratio would be the triangle that has an opposite side of length 3 and a hypotenuse of length 4.

Determining all of the side lengths and angle measures of a right triangle is known as solving a right triangle.

It has an opposite side of length 2 and an adjacent side of length 5.

You could have used a triangle that has an opposite side of length 4 and an adjacent side of length 10. In this right triangle, because , the ratio of the opposite side to the hypotenuse is .

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.

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