Question

find p.
write your answer as an integer or as a decimal rounded to the nearest tenth.
p =
submit

Explanation:

Step1: Find angle at Q

The sum of angles in a triangle is \(180^\circ\). So, \(\angle Q = 180^\circ - 31^\circ - 85^\circ = 64^\circ\).

Step2: Apply Law of Sines

Law of Sines states \(\frac{p}{\sin P}=\frac{PQ}{\sin R}\). Here, \(P = 31^\circ\), \(PQ = 10\), \(R = 85^\circ\).
So, \(\frac{p}{\sin 31^\circ}=\frac{10}{\sin 85^\circ}\).

Step3: Solve for p

\(p=\frac{10\times\sin 31^\circ}{\sin 85^\circ}\).
Calculate \(\sin 31^\circ\approx0.5150\), \(\sin 85^\circ\approx0.9962\).
Then \(p=\frac{10\times0.5150}{0.9962}\approx\frac{5.15}{0.9962}\approx5.2\).

Answer:

\(5.2\)