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Chapter 8: Q. 11 (page 535)

Solve the triangle

Short Answer

Expert verified

The solution is

$c = 3.75, A = 29.54 °, B = 55.46 °$

Step by step solution

01

Step1. Given information

The figure is

02

Step2. Formula used

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

03

Step3. Calculation

$W e h a v e, a = 2, b = 3, C = 95 ° W e k n o w c^{2} = a^{2} + b^{2} - 2 a b . \cos C = 2^{2} + 3^{2} - 2.2.3 . \cos 95 ° = 4 + 9 - 12 (- . 087) = 13 + 1.044 = 14.044 c = \sqrt{14.044} = 3.75 A g a i n, \cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} = \frac{3^{2} + {(3.75)}^{2} - 2^{2}}{2.3 . (3.75)} = \frac{9 + 14.0625 - 4}{22.5} = \frac{19.0625}{22.5} = 0.87 A = \cos^{- 1} (0.87) = 29.54 ° A g a i n w e k n o w A + B + C = 180 ° 29.54 ° + B + 95 = 180 ° B = 180 ° - 124.54 ° = 55.46 °$

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Most popular questions from this chapter

Find an exact value of each expression, without using a calculator $\cos^{2} 40 + \cos^{2} 50$

In the given problem solve the triangle using either the law of sines or law of cosines-

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the displacement d (in meters) of an object at time t (in seconds) is given $d = 6 + 2 \cos (2 π t)$

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See all solutions

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