Solving Right Triangles Word Problems

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?

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.

Solving Right Triangles Word Problems-88Solving Right Triangles Word Problems-42

To the nearest foot, how many feet of string has Emma let out?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.Note that the hypotenuse is twice as long as the shortest leg which is opposite the 30° angle, so that .The length of the longest leg which is opposite the 60Since we know all the measures of the angles, we now need to find the lengths of the missing sides.Solving the equation and rounding to the nearest tenth gives you Sometimes you may be given enough information about a right triangle to solve the triangle, but that information may not include the measures of the acute angles.In this situation, you will need to use the inverse trigonometric function keys on your calculator to solve the triangle.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.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.

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