Calculating angles in a triangle
We can use trigonometric identities to calculate angles as well as the lengths of sides. In order to calculate angles we must know two sides of the right-angled triangle. Look at this triangle:
We want to know the angle at C. Take a look at the cos equation:
\({cos~θ} = \frac {adjacent} {hypotenuse}\)
We do not know θ, but we do know that \({cos~θ} = \frac {5} {7}\)
We can use the inverse cos function on a calculator to work out what θ is if we know cos θ.
Use the cos-1 button (by pressing SHIFT then cos) on the calculator, followed by (5 ÷ 7) and then press =
You should get the answer 44.42° (to two decimal places).
Question
Find the angle at Z.
Since we know the length of the hypotenuse and the opposite side, we need to use sin.
\({sin~θ} = \frac {opposite} {hypotenuse}\)
So, by substitution, \({sin~θ} = \frac {5} {8}\)
We need to use the inverse sin function on the calculator to work out what θ is.
Using the sin-1 button (by pressing SHIFT then sin) on the calculator followed by (5 ÷ 8) gives us 38.68° (to two decimal places).
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