Q66 / 160 · TS EAMCET 2022 (20 Jul Shift 2) · Mathematics

In triangle $\mathrm{ABC}$, if $a=7, b=8, \mathrm{C}=\frac{3 \sqrt{5}}{2}$ and $\mathrm{C}$ is an acute angle, then $c=$

  • A
    $\sqrt{145}$
  • B
    5
  • C
    11
  • Correct answer
    D
    9

Solution

$\begin{aligned} & \text { } \tan \mathrm{c}=\frac{3 \sqrt{5}}{2} \\ & \Rightarrow \cos \mathrm{C}=\frac{2}{7} \\ & \cos \mathrm{c}=\frac{\mathrm{a}^2+\mathrm{b}^2-\mathrm{c}^2}{2 \mathrm{ab}} \\ & \Rightarrow \frac{2}{7}=\frac{49+64-\mathrm{c}^2}{2.7 .8} \\ & \Rightarrow 32=113-\mathrm{c}^2 \\ & \Rightarrow \mathrm{c}^2=113-32=81 \\ & \Rightarrow \mathrm{c}=9\end{aligned}$

Hence, the correct answer is option: 'D'.

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