Chapter 8: Q. 17 (page 535)

Solve the triangle
a = 3, b = 4, C = 40 $°$

Short Answer

Expert verified

The solution is

$c = 2.55, A = 48.7 °, B = 91.3 °$

Step by step solution

Step1. Given information

$a = 3, b = 4, C = 40 °$

Step2. Formula used

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

Step3. Calculation

$W e k n o w c^{2} = a^{2} + b^{2} - 2 a b . \cos C = 3^{2} + 4^{2} - 2.3.4 . \cos 40 ° = 9 + 16 - 24 . (. 77) = 25 - 18.48 = 6.52 c = \sqrt{6.52} = 2.55 A g a i n, \cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} = \frac{4^{2} + {(2.55)}^{2} - 3^{2}}{2.4 . (2.55)} = \frac{16 + 6.52 - 9}{20.4} = \frac{13.52}{20.4} = . 66 A = \cos^{- 1} (. 66) = 48.7 ° w e k n o w, A + B + C = 180 ° 48.7 ° + B + 40 ° = 180 ° B = 180 ° - 88.7 ° = 91.3 °$

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Solve the triangle
a = 3, b = 4, C = 40 $°$

Short Answer

Step by step solution

Step1. Given information

Step2. Formula used

Step3. Calculation

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Solve the trianglea = 3, b = 4, C = 40°

Short Answer

Step by step solution

Step1. Given information

Step2. Formula used

Step3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Calculus

Mechanics Maths

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve the triangle
a = 3, b = 4, C = 40 $°$