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Deduce exact trigonometric ratios from one ratio

DIFFICULTYintrostandardchallengeexam
QUESTION TYPEMix of allChange
sin:integer:integer:cos:nonesin:integer:integer:tan:nonecos:integer:integer:sin:nonecos:integer:integer:tan:nonetan:integer:integer:sin:nonetan:integer:integer:cos:noneNOWMix of allRecommended
Question 1 of 8

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A right-angled triangle has the acute angle under consideration

For the marked angle \(\theta\), \(\tan\theta=\frac{5}{12}\)

Use side lengths \(5\) and \(12\) in numerator and denominator order for the given ratio

Right-angled triangle with a horizontal base and a vertical side on the right. The right angle is marked at the lower-right vertex. An arc marks the acute angle theta at the left vertex, between the horizontal and sloping sides. The vertical side is labelled 5 and the horizontal side is labelled 12. The sloping side has no length label.125θ
The two labels give proportional side lengths for the stated ratio — use the given values, not measurements from the diagram
1 mark

Calculate \(\sin\theta\) from the given ratio, giving an exact value

For a value containing a square root, use the canonical form \((P\pm Q\sqrt{R})/S\) and enter its labelled coefficients