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Chapter 8: Q. 16 (page 535)

Solve the triangle

Short Answer

Expert verified

The solution is $A = 67.98 °, B = 44.04 °, C = 67.98 °$

Step by step solution

01

Step2. Given information

$H e r e, a = 4, b = 3, c = 4$

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

We know

$\cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} = \frac{3^{2} + 4^{2} - 4^{2}}{2.3.4} = \frac{9 + 16 - 16}{24} = \frac{9}{24} = . 375 A = \cos^{- 1} (. 375) = 67.98 ° A g a i n, \cos B = \frac{a^{2} + c^{2} - b^{2}}{2 a c} = \frac{4^{2} + 4^{2} - 3^{2}}{2.4.4} = \frac{16 + 16 - 9}{32} = \frac{23}{32} = . 71875 B = \cos^{- 1} (. 71875) = 44.04 ° W e k n o w, A + B + C = 180 ° 67.98 ° + 44.04 ° + C = 180 ° C = 180 ° - 112.02 = 67.98 °$

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Most popular questions from this chapter

Find the area of the triangle. Round answer to two decimal places.

$A = 110 °, C = 30 °, c = 3$

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