Chapter 9 Review

I am going back to Chapter 9 because these types of problems are often found on the ACT andI know I sometimes struggle with them. In Chapter 9, section 1 we learn how to solve right triangles. This lesson is a simple repeat of what we had learned in geometry. To help solve these problems and make memorizing the formulas easier you must remember SOHCAHTOA.

SOHCAHTOA is:
Sin (S)= opposite (O)/hypotenuse (H)
Cos (C)= adjacent (A)/hypotenuse (H)
Tan (T)= opposite (O)/adjacent (A)

Once you can remember SOHCAHTOA, you can remember all the formulas. Secant is the reciprocal of sine, cosecant is the reciprocal of cosine, and cotangent is the reciprocal of tangent.When looking at a triangle, opposite is the degrees across from the angle already given to you. The degrees already attached to the given is the adjacent angle, and hypotenuse is ALWAYS the degrees across from the right angle.

To solve a problem, draw your triangle and plug in the points and angles given to you. Some triangles may be named. Once you have drawn the triangle, find what they are asking you to solve (the missing angles or points), and you look for the appropriate formula. Once you have a degree to each angle you are done. Make sure to label all angles and points on the triangle, if you want credit.

Solve the triangle QRS.
Angle R- 34degrees Side r- 26 degrees Angle Q- 90 degrees
Those are the angles given, so you need to find angle and sides q, S, and s.

In order to find S, simply subtract 180-90-34 to compose an answer.
Angle S= 56 degrees
In order to find q, use the formula for sin which is opposite/ hypotenuse
Angle q= 46.496 degrees
In order to find s, use the formula for tan, which is opposite/ adjacent
Angle s= 38.547 degrees