If cos $\theta$ = $\frac{4}{5}$ then tan $\theta$ = ?

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KollegeApply · Accepted Answer

bb($\frac{3}{4}$) Explanation: cos $\theta$ = $\frac{4}{5}$ $\Rightarrow$ (AB)/(AC) = $\frac{4}{5}$ Let AB = 4k and AC = 5k. Then, BC2 = (AC2 – AB2) = (25k2 – 16k2) = 9k2 $\Rightarrow$ BC = sqrt(9k^2) $\Rightarrow$ BC = 3k. $\therefore$ tan $\theta$ = (BC)/(AB) = (3k)/(4k) = $\frac{3}{4}$ [Solution diagram: 470321_solution_1.png]

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