Exercise 3 Page 557

Let's consider a right triangle for which we know the lengths of the sides.

In order to find the measures of the acute angles, we first check if we are dealing with a special right triangle.

1. If the triangle is isosceles, both acute angles are congruent and complementary. Therefore, they have a measure of 45^(∘) each. In this case we get a 45^(∘)-45^(∘)-90^(∘) triangle.
   
2. If the length of the hypotenuse is twice the length of the shorter leg or if the length of the longer leg is sqrt(3) times the length of the shorter leg, then the triangle is a 30^(∘)-60^(∘)-90^(∘) triangle.

On the other hand, if the triangle is none of the special triangles mentioned above, we can find the angle measures by using a calculator. To do that, we first find the sine, cosine, or tangent of the wanted angle. sin A or cos A or tan A Then, we use the inverse sine, inverse cosine, or inverse tangent feature on the calculator to approximate the measure of the angle.