04Efindingangles

toc = Trigonometry =

Finding Angles
Recall that the basic rules for trigonometry are:



To find the angle:
 * identify which two sides are involved in the problem
 * identify which of the 3 trig rules includes those two sides
 * write down the relevant trig rule
 * substitute the information that is known
 * use your calculator to find the value of the angle
 * check your calculator is in DEGREES mode
 * use ** [2nd] ** to get the inverse function
 * use brackets around the division
 * round to a sensible number of decimal places (or write in Dº M' S" if asked)
 * write the answer (include the degrees sign)

** Example 1 **
**(a)** Find the value of a in the triangle shown: __**Solution:**__

{the two sides involved are ADJ and HYP so use __**cos**__}

math \\ . \qquad \cos \big( \theta \big) = \dfrac{\text{ADJ}}{\text{HYP}} \\ \\ \\ . \qquad \cos \big( \alpha \big) = \dfrac{8.5}{9} \\ \\ . \qquad \alpha = \cos^{-1} \left( \dfrac{8.5}{9} \right) \\ \\ . \qquad \alpha = 19.2^\circ math

__**Solution:**__
 * (b) ** Find the value of b in the triangle shown:

{the two sides involved are OPP and ADJ so use __**tan**__} math \\ . \qquad \tan \big( \theta \big) = \dfrac{\text{OPP}}{\text{ADJ}} \\ \\ \\ . \qquad \tan \big( \beta \big) = \dfrac{4.7}{8.3} \\ \\ . \qquad \beta = \tan^{-1} \left( \dfrac{4.7}{8.3} \right) \\ \\ . \qquad \beta = 29.5^\circ math

Checking Answers
You can check your answer for how sensible it is:
 * the proportion of the two sides should give you a feel for the size of the angle
 * look at the actual lengths, don't trust the diagram - they are rarely drawn to scale

If your answer doesn't seem sensible, you may have made a mistake.

**For example:**

In Eg 1a (above)
 * The adjacent side is only a little smaller than the hypotenuse
 * so we expect a fairly small angle
 * Actual answer was 19.2º so that seems sensible

For another site that explains this idea, go here: MathsIsFun

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