In triangle mathrm{PQR}, p=99 mathrm{~cm}, r=97 mathrm{~cm} and angle mathrm{R}=112^{circ}. Find all possible values of angle mathrm{P}, to the nearest degree.

Question

Accepted Answer

Step:1 ：Use the Law of Cosines to find the length of side q: (q = sqrt{p^2 + r^2 - 2pr cos{R}})Step:2 ：Use the Law of Sines to find the angle P: (frac{sin{P}}{p} = frac{sin{R}}{r})Step:3 ：Calculate the values: (q = sqrt{99^2 + 97^2 - 2(99)(97) cos{112^circ}} approx 162.50)Step:4 ：Calculate the angle P: (sin{P} = frac{99 sin{112^circ}}{97} Rightarrow P approx 34.39^circ)Step:5 ：boxed{text{Final Answer: } P approx 34^circ}

Answer

Step: 1 ：Use the Law of Cosines to find the length of side q: (q = sqrt{p^2 + r^2 - 2pr cos{R}})Step: 2 ：Use the Law of Sines to find the angle P: (frac{sin{P}}{p} = frac{sin{R}}{r})Step: 3 ：Calculate the values: (q = sqrt{99^2 + 97^2 - 2(99)(97) cos{112^circ}} approx 162.50)Step: 4 ：Calculate the angle P: (sin{P} = frac{99 sin{112^circ}}{97} Rightarrow P approx 34.39^circ)Step: 5 ：boxed{text{Final Answer: } P approx 34^circ}

In $△ PQR, p = 99 cm, r = 97 cm$ and $∠ R = 112^{\circ}$ . Find all possible values of $∠ P$ , to the nearest degree.

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Popular Problems

In △PQR,p=99 cm,r=97 cm and ∠R=112∘. Find all possible values of ∠P, to the nearest degree.

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Popular Problems

In $△ PQR, p = 99 cm, r = 97 cm$ and $∠ R = 112^{\circ}$ . Find all possible values of $∠ P$ , to the nearest degree.