Find all other trigonometrical ratios in triangle PQR, angle Q=90degre

1.	Find all other trigonometrical ratios in triangle PQR, angle Q=90degree and tan=3/4
Answer» If Tan A\xa0=\xa03/4, then find the other trigonometric ratio of angle\xa0A.sol) Tan A\xa0=\xa0Opposite side\xa0=\xa03 Adjacent side 4.^., opposite side : adjacent side = 3:4For angle\xa0A,\xa0opposite side\xa0=\xa0BC=3kAdjacent side\xa0=AB=4k(where\xa0k\xa0is any +ve no)Now, we have in triangle\xa0ABC(\xa0by Pythagoras theorem)\xa0\xa0AC^2\xa0=\xa0AB^2 + BC^2=>(3k)^2 + (4k)^2\xa0=\xa025k^2AC\xa0=\xa0√25k^2=> 5k\xa0=\xa0Hypotenuse\xa0Now,we can easily write the other ratios of trigonometrysin A\xa0=\xa03k\xa0=\xa03 5k 5cos A\xa0=\xa04k\xa0=\xa04 5k 5cosec A\xa0=\xa0 1 = 5 sin A 3sec A\xa0=\xa0 1 = 5 cos A 4cot A\xa0=\xa0 1 = 4 tan A 3

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