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1 of 8 0-day streak

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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Let the marked angle be acute in a right-angled triangle

For the marked angle \(\theta\), \(\sin\theta=\frac{20}{29}\)

Use side lengths \(20\) and \(29\) 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 20 and the sloping side is labelled 29. The horizontal side has no length label.2029θ
The two labels give proportional side lengths for the stated ratio — use the given values, not measurements from the diagram
1 mark

Deduce the exact value of \(\tan\theta\)

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