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Chapter 6: Problem 17

Solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. $$a=5, b=7, c=10$$

Short Answer

Expert verified
Based on the calculations, we get angle A as 34 degrees, angle B as 47 degrees, and angle C as 99 degrees. Remember, you will need to round the angles to the nearest degree. These are the measures of the angles of the triangle with sides (a=5, b=7, c=10).

Step by step solution

01

- Calculating Angle A

We can calculate the first angle, say angle A, using the Law of Cosines. The formula will be \( cos(A) = \frac{{b^2 + c^2 - a^2}}{{2bc}} \). Substituting our given sides, we get \( cos(A) = \frac{{7^2 + 10^2 - 5^2}}{{2 * 7 * 10}} \). Calculate the numbers inside the cosine to find \( cos(A) = \frac{74}{70} \). To find angle A, take the inverse cosine of \( \frac{74}{70} \), resulting in \( A = cos^{-1}(\frac{74}{70}) \).
02

- Calculating Angle B

Now, to find angle B, we can use the Law of Cosines again. The formula would be \( cos(B) = \frac{{a^2 + c^2 - b^2}}{{2ac}} \). Substituting the given sides, we get \( cos(B) = \frac{{5^2 + 10^2 - 7^2}}{{2 * 5 * 10}} \). Calculate the numbers inside the cosine to get \( cos(B) = \frac{56}{100} \). To find angle B, take the inverse cosine of \( \frac{56}{100} \), resulting in \( B = cos^{-1}(\frac{56}{100}) \).
03

- Calculating Angle C

Knowing the sum of angles in a triangle is 180 degrees, we can subtract the sum of angles A and B from 180 to find angle C. So, \( C = 180 - A - B \). After calculating, round to the nearest degree.

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Most popular questions from this chapter

Will help you prepare for the material covered in the next section. Refer to Section 2.1 if you need to review the basics of complex numbers. In each exercise, perform the indicated operation and write the result in the standard form \(a+b i\). $$\frac{2+2 i}{1+i}$$

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