Triangle problems

I have found that in large tests such as the Ohio Graduation Test, students often have trouble recognizing how to solve different problems involving right triangles. Scenarios involving right triangles are abundant in such tests, and it is vital for students to be able to approach these problems with confidence.

I am challenging my students to recognize and differentiate between the following scenarios: (1) when they know two sides of a right triangle, (2) when they know one angle and one side of a right triangle, and (3) when they know two angles. Furthermore, I am challenging them to assess what they need to find, whether it is (1) the length of a side, (2), the area of a triangle, or (3) the measurement of an angle.

I am confident that if my students become familiar with differentiating between these scenarios, they will be able to recognize when they need to use the Pythagorean Theorem, trigonometric ratios, or other geometric properties of triangles to solve a problem.