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agasfer [191]
3 years ago
10

In ΔABC, the lengths of a, b, and c are 22.5 centimeters, 18 centimeters, and 13.6 centimeters, respectively.

Mathematics
2 answers:
ehidna [41]3 years ago
8 0

Answer:

It is not 37.19 and 53.13.

Step-by-step explanation:

For newcomers who are using PLATO, I recently finished the test, and it is not the answer below. I don't know the right answer, unfortunately.

Irina-Kira [14]3 years ago
7 0
Given the values of the three sides of the triangle, we can apply the Cosine Law to find the angles of the triangle. Recall that for we can express the value of c through the equation below.

c^{2} = a^{2} + b^{2} - 2abcosC

Rearranging this equation, we can find the value ∠C as shown below.

\cos C = \frac{a^{2}+b^{2}-c^{2}}{2ab}
C = cos^{-1} (\frac{a^{2}+b^{2}-c^{2}}{2ab})

We can apply the same reasoning for finding the value of ∠B as shown.

B = cos^{-1} (\frac{a^{2}+c^{2}-b^{2}}{2ac})

Plugging in the values of the sides (see image attached) from the given. It will now be straightforward to compute for ∠B and ∠C.

C = cos^{-1} (\frac{22.5^{2}+18^{2}-13.6^{2}}{2(22.5)(18)})
C \approx 37.19

B = cos^{-1} (\frac{22.5^{2}+13.6^{2}-18^{2}}{2(22.5)(13.6)})
B \approx 53.13

Answer: ∠C = 37.19° and ∠B = 53.13°

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