In /_\NOP,p=760 inches, o=710 inches and /_O=124^(@). Find all possible values of /_P, to the nearest degree. Answer:

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In  /_\NOP,p=760 inches,  o=710 inches and  /_O=124^(@). Find all possible values of  /_P, to the nearest degree. Answer:

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Use Law of Sines: To find the possible values of angle P, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the opposite angle is the same for all three sides and angles. The formula is given by:  $$ \frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)} $$  where a, b, and c are the lengths of the sides, and A, B, and C are the opposite angles. In this case, we have side o (710 inches) opposite angle O (124 degrees), and side p (760 inches) opposite angle P. We can set up the equation as follows:  $$ \frac{710}{\sin(124^\circ)} = \frac{760}{\sin(P)} $$  Now we need to solve for sin(P).Calculate Sine of Angle O: First, we calculate the sine of angle O:  $$ \sin(124^\circ) $$  Using a calculator, we find that:  $$ \sin(124^\circ) \approx 0.81915204 $$  Now we can substitute this value into our equation:  $$ \frac{710}{0.81915204} = \frac{760}{\sin(P)} $$  Next, we solve for sin(P).Substitute Values: We calculate the left side of the equation:  $$ \frac{710}{0.81915204} \approx 866.0254 $$  Now we have:  $$ 866.0254 = \frac{760}{\sin(P)} $$  To find sin(P), we rearrange the equation:  $$ \sin(P) = \frac{760}{866.0254} $$  Now we calculate sin(P).Solve for Sin(P): We calculate sin(P):  $$ \sin(P) \approx \frac{760}{866.0254} \approx 0.87719298 $$  Since the sine function can have two different angles that have the same sine value (one acute and one obtuse), we need to find the angle P that corresponds to this sine value. We use the inverse sine function to find the acute angle first.Find Acute Angle P: Using a calculator, we find the acute angle P:  $$ P \approx \sin^{-1}(0.87719298) $$  $$ P \approx 61^\circ $$  However, since the sum of angles in any triangle must be 180 degrees, we need to check if there is another possible value for angle P by subtracting the acute angle from 180 degrees.Calculate Obtuse Angle: We calculate the possible obtuse angle for P:  $$ P_{obtuse} = 180^\circ - P_{acute} $$  $$ P_{obtuse} = 180^\circ - 61^\circ $$  $$ P_{obtuse} = 119^\circ $$  However, we must remember that the sum of the angles in a triangle must be 180 degrees. Since we already have two angles (124 degrees and 61 degrees), adding a third angle of 119 degrees would exceed 180 degrees. Therefore, the obtuse angle is not a possible solution for this triangle.Check Triangle Sum: We conclude that the only possible value for angle P is the acute angle we found:  $$ P \approx 61^\circ $$  We round this to the nearest degree as requested.

In $\triangle \mathrm{NOP}, p=760$ inches, $o=710$ inches and $\angle \mathrm{O}=124^{\circ}$ . Find all possible values of $\angle \mathrm{P}$ , to the nearest degree. $\newline$ Answer:

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In △NOP,p=760 \triangle \mathrm{NOP}, p=760 △NOP,p=760 inches, o=710 o=710 o=710 inches and ∠O=124∘ \angle \mathrm{O}=124^{\circ} ∠O=124∘. Find all possible values of ∠P \angle \mathrm{P} ∠P, to the nearest degree.\newlineAnswer:

In $\triangle \mathrm{NOP}, p=760$ inches, $o=710$ inches and $\angle \mathrm{O}=124^{\circ}$ . Find all possible values of $\angle \mathrm{P}$ , to the nearest degree. $\newline$ Answer: