Question

ry 1. In ∆ABC, if B = 90°, AB = 12 cm and BC = 9 cm, then the value of cos C is

Options:

9/15
3/4
5/3
4/3​

Answer 1

Step-by-step explanation:

We have to apply cos rule two times

$\cos( \beta ) = \frac{c^{2} + {a}^{2} - {b}^{2} }{2ac} \\ \cos(90) = \frac{ {12}^{2} + {9}^{2} - {b}^{2} }{2ac} \\ {12}^{2} + {9}^{2} - {b}^{2} = 0 \\ = > {b}^{2} = {12}^{2} + {9}^{2} \\ = > b = \sqrt{144 + 81} \\ b = \sqrt{225} \\ b = 15$

Now ;

$\cos(c) = \frac{ {a}^{2}+ {b}^{2} - {c}^{2} }{2ab} \\ = \frac{ {12}^{2} + {15}^{2} - {9}^{2} }{2.12.15 } \\ = \frac{144 + 225 - 81}{360} \\ = \frac{288}{360} \\ = \frac{4}{5} \\ \cos(c) = \frac{4}{5}$

All the given options are wrong.

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Answer 2

Answer:

please check the question.