Question

find the tangent of ∠p. simplify your answer and write it as a proper fraction, improper fraction, or wh tan (p) =
(there is a right triangle prq with right angle at r, pr = 8, pq = 17)

Explanation:

Step1: Find side length QR

Use Pythagorean theorem:
$$QR = \sqrt{PQ^2 - PR^2} = \sqrt{17^2 - 8^2} = \sqrt{289 - 64} = \sqrt{225} = 15$$

Step2: Define tangent of ∠P

Tangent = opposite/adjacent:
$$\tan(P) = \frac{QR}{PR}$$

Step3: Substitute values

Plug in side lengths:
$$\tan(P) = \frac{15}{8}$$

Answer:

$\frac{15}{8}$