The sides and angles of right triangles always have some relationships between them in common. These constants allow you to figure out the measures of some angles and the length of some sides using less information than may at first seem necessary.
Before learning these relationships you need to be familiar with how these sides (or legs) of a triangle may be referred to on the GED math test when there is a question related to trigonometry.
The hypotenuse is always the hypotenuse, but the two legs of a triangle are named depending on where they are from the angle you are referring to. Both legs will be either termed a “side adjacent” or a “side opposite” depending on where they stand in relation to either angle B or angle C. The right angle, in this case A, is not used to refer to legs in trigonometry.
Look at ∠B in the image. The leg that runs into ∠B is line AB and is ∠B’s adjacent side. Across the triangle from ∠B is AC, and this is the opposite side of ∠B. Likewise, side AB is ∠C’s opposite side and AC is the adjacent side to ∠C.
You can use three trigonometric ratios to help you solve for missing side lengths and angle measurements. The formulas of these three ratios will be provided to you during the test on the formula sheet.
The ratio of a triangle depends on which of the two non right angles is being referenced, so every triangle has two sine ratios, two cosine ratios and two tangent ratios.
The sine of ∠B in the triangle above is the side opposite ∠B over the hypotenuse:
The sine of ∠C in the triangle above is the side opposite ∠C over the hypotenuse:
The cosine of ∠B in the triangle above is the line adjacent to ∠B over the hypotenuse.
The cosine of ∠C in the triangle above is the line adjacent to ∠C over the hypotenuse.
The tangent of ∠B in the triangle above is the line opposite to ∠B over the line adjacent to ∠B.
The tangent of ∠C in the triangle above is the line opposite to ∠C over the line adjacent to ∠B.
Applying Trigonometric Ratios
These trigonometric ratios might at first seem pretty useless, however they can be very helpful when you want to find a missing value in a right triangle, which could come up on the GED math test.
When applying trigonometric ratios you will probably need a calculator that has the sin, cos and tan buttons, which the one you will be given during the test does.
Here is an example of how to apply a trigonometric ratio. Let’s say you are shown this image and asked to find the length of the base of the triangle.
To decide if you should use sine, cosine or tangent, think about the information you have and the information you need. You have the measure of one angle (besides the right angle), and the leg adjacent to that angle. You need the measure of the leg opposite that angle. Since your calculation will have to do with the legs of the triangle and not the hypotenuse, you will use tangent. Sine and cosine are for when you have or want to know the length of the hypotenuse. Your equation should look like this:
Now to get tan 50°, just hit 50 then the “tan” button on your calculator: about 1.19
Now solve for b.
The length of the base in the above triangle is 9.52 feet.