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Chapter 8: Q. 15 (page 535)

Solve the triangle

Short Answer

Expert verified

The solution is

$a = 127.17 °, B = 32.86 °, C = 19.97 °$

Step by step solution

01

Step.1 Given information

02

Step2. Formula used

$\cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c}, \cos B = \frac{a^{2} + c^{2} - b^{2}}{2 a c}$

03

Step3. Calculation

$W e k n o w, \cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} = \frac{6^{2} + 4^{2} - 9^{2}}{2.6.4} = \frac{36 + 16 - 81}{48} = \frac{- 29}{48} = - . 6042 A = \cos^{- 1} (- . 6042) = 127.17 ° A g a i n \cos B = \frac{a^{2} + c^{2} - b^{2}}{2 a c} = \frac{9^{2} + 4^{2} - 6^{2}}{2.9.4} = \frac{81 + 16 - 36}{72} = \frac{61}{72} = . 84 B = \cos^{- 1} (. 84) = 32.86 ° A g a i n w e k n o w, A + B = C = 180 ° 127.17 ° + 32.86 ° + C = 180 ° C = 180 ° - 160.03 = 19.97 °$

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