Math A

Right Triangle
Trigonometry
Solving for a Side

 

Basic Trigonometry Rules:

  • These formulas ONLY work in a right triangle.

  • The hypotenuse is across from the right angle.

  • Questions usually ask for an answer to the nearest units.

  • You need a scientific or graphing calculator.

 

Formulas:

where A represents the angle of reference.
 

The formulas can be remembered by:
oh heck, another hour of algebra!

The formulas can be remembered by:
oscar had a heap of apples

There are many such memory devices!


How to set up and solve a trigonometry problem:

In right triangle ABC, hypotenuse AB=15 and angle A=35º.
Find leg BC to the nearest tenth.

Set Up:
  1. Draw a picture depicting the situation.
  2. Be sure to place the degrees INSIDE the triangle.
  3. Place a stick figure at the angle as a point of reference.
  4. Thinking of yourself as the stick figure, label the opposite side (the side across from you), the hypotenuse (across from the right angle), and the adjacent side (the leftover side).
  5. Notice how the items on the sides of the triangle pair up.  The h pairs with the 15, the o pairs with the x, but the a stands alone.  The a has no companion term.  This means that the a is NOT involved in the solution of this problem.  Cross it out!
  6. This problem deals with o and h which means it is using sin A.

Answer:

 Solution:
  1. Place the degrees in the formula for angle A.
  2. Replace o and h with their companion terms.
  3. Using your scientific/graphing calculator, determine the value of the left side of the equation.  (On most scientific calculators, press 35 first and then press the sin key.  On most graphing calculators, press the sin key first and the 35 second.)
  4. Solve the equation algebraically.  Cross multiply and solve for x.  Or just remember that if the x is on the top, you will multiply to arrive at your answer.  If x is on the bottom, divide to arrive at your answer (see next example).
  5. Round answer to the desired value.

 

Another Example:

In right triangle ABC, leg BC=20 and angle B = 41º.
Find the hypotenuse BA to the nearest hundredth.

  
Hint: If you are having a problem solving the equation algebraically, remember that when x is on the bottom, you must divide to arrive at your answer.  The division is always "divide BY the decimal". Hint:  Be sure your answer MAKES SENSE!!!  The hypotenuse is always the largest side in a right triangle.  So, our answer of 26.50 makes sense - it is bigger than the leg of 20.

 

You really know a lot of facts about these triangles:

 In this triangle, you were given the values in black.  You also know that the angle at B is 68º because there are 180º in every triangle.   By repositioning your reference point, all of the following are true.  

How to use your
TI-83+ graphing calculator  with beginning trigonometry.
Click calculator.

 

 

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Roberts