# 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.

## Comments Solving Right Triangles Word Problems

• ###### Trig Word Problems #1 Trigonometry - Right Triangles

Trig Word Problems #1 Reference Mathematics Trigonometry Trigonometry - Right Triangles Now that we have a basic understanding of what the trig functions sine, cosine, and tangent represent, and we can use our calculators to find values of trig functions, we can use all of this to solve some word problems.…

• ###### Right Triangle Applications - uga.edu

Right triangle geometry has many applications in the real world. Carpenter use it to make cabinets, surveyors use it in their work, you can use what you've learned to measure tall structures. In this lesson you will use what you have learned to solve problems.…

• ###### Learn Pythagorean Theorem Problems Solving Right Triangles

Pythagorean Theorem Word Problems. Word problems using the Pythagorean theorem require you to draw or imagine a right triangle where two of the sides are of known length. When solving these problems, remember the following The diagonal across a rectangle creates two congruent right triangles.…

• ###### Solving SSA Triangles - Maths Resources

Note there is only one answer in this case. The "12.4" line only joins up one place. The other possible answer for L is 149.9°. But that is impossible because we already have M = 125° and a triangle can't have two angles greater than 90°.…

• ###### Braingenie Solving Right Triangles Overview

Use trigonometric identities to transform the left side of the equation into the right side Solving Right Triangles. Word Problems – Angle of Elevation…

• ###### Awesome Word Problems To Engage Students

A key to differentiated instruction, word problems that students can relate to and contextualize will capture interest more than generic and abstract ones. Final Thoughts about Math Word Problems. You’ll likely get the most out of this resource by using the problems as templates, slightly modifying them by applying the above tips.…