Calculating a length
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The three trigonometric ratios can be used to calculate the length of a side in a right-angled triangle.
Example
Calculate the length AB. Give the answer to one decimal place.
Label the sides of the triangle \(o\), \(a\) and \(h\).
Next choose the correct ratio from \(s^o_h~c^a_h~t^o_a\).
The length \(h\) is known and the length \(o\) must be calculated.
Use \(\sin{x} = \frac{o}{h}\)
\(\sin{32} = \frac{AB}{8}\)
Make AB the subject by multiplying both sides by 8.
AB = \(8 \times \sin{32}\)
AB = 4.2 cm
It may be necessary to rearrange the formula to calculate a length.
Question
Calculate the length YZ. Give the answer to one decimal place.
Label the sides of the triangle \(o\), \(a\) and \(h\).
Next choose the correct ratio from \(s^o_h~c^a_h~t^o_a\).
The length \(a\) is known and the length \(h\) must be calculated.
Use: \(\cos{x} = \frac{a}{h}\)
\(\cos{25} = \frac{5}{\text{YZ}}\)
Rearrange the equation to make YZ the subject.
Multiply both sides by YZ.
\(\text{YZ} \times \cos{25} = 5\)
Divide both sides by \(\cos{25}\).
YZ = \(\frac{5}{\cos{25}}\)
YZ = 5.5 cm
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