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Chapter 5: Problem 12

Use the Law of Cosines to solve the triangle. Round your answers to two decimal places. $$a=1.42, \quad b=0.75, \quad c=1.25$$

Short Answer

Expert verified
The calculated values of angles \(A\), \(B\), and \(C\) will be the solution to the exercise, each rounded to two decimal places.

Step by step solution

01

Calculation of Angle C (opposite side c)

By applying the law of cosines, we can compute angle \(C\) using the formula: \[ C = \cos^{-1}\left( \frac{{a^2+b^2-c^2}}{{2ab}} \right) \] After substituting with given values: \[ C = \cos^{-1}\left( \frac{{1.42^2+0.75^2-1.25^2}}{{2*1.42*0.75}} \right) \] When evaluated, we obtain the value of angle \(C\).
02

Calculation of Angle A (opposite side a)

Subsequently, we compute angle \(A\) using the formula: \[ A = \cos^{-1}\left( \frac{{b^2+c^2-a^2}}{{2bc}} \right) \] After substituting with given values: \[ A = \cos^{-1}\left( \frac{{0.75^2+1.25^2-1.42^2}}{{2*0.75*1.25}} \right) \] When computed, we obtain the value of angle \(A\).
03

Calculation of Angle B (opposite side b)

Finally, we calculate angle \(B\) using the property that the sum of all angles in a triangle is 180掳: \[ B = 180掳 - (A + C) \] After filling in the previously calculated angles \(A\) and \(C\), we obtain the value of angle \(B\).

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Most popular questions from this chapter

Consider the function given by \(f(x)=3 \sin (0.6 x-2)\). (a) Approximate the zero of the function in the interval [0,6] (b) A quadratic approximation agreeing with \(f\) at \(x=5\) is \(g(x)=-0.45 x^{2}+5.52 x-13.70 .\) Use a graphing utility to graph \(f\) and \(g\) in the same viewing window. Describe the result. (c) Use the Quadratic Formula to find the zeros of \(g\). Compare the zero in the interval [0,6] with the result of part (a).

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