Page 247 - ABCTE Study Guide_Neat

We’re given an angle measure and the side adjacent to that angle. We want to find the length of the side
opposite the given angle. So, we need a trig formula that relates the measure of an angle to the sides
opposite and adjacent to that angle. The tangent function does that with the following:

Now, evaluate tan30° on a scientific calculator to get tan30°=0.58.

So the height of the triangle is about 5.8 in.

Example 2: Now let’s find the length of the hypotenuse. We could use the fact that there are 180° in a
triangle to find the measure of the other acute angle, or we could simply use the angle we’re given. If we
do that, we have an angle and the sides opposite and adjacent to it. We want to find the hypotenuse, so
we could use either sine or cosine.

Now evaluate cos30° on a scientific calculator to get cos30° = 0.87.

Therefore, the , or about 11.5 in.