Question

for the triangle shwon rp=12 and dr=16 which of the following is the correct way to set up the problem to find dp

Answer 1

I don’t have the picture or the answer choices, so I can’t pick one for you. Which setup is correct depends on where the right angle (or other given angle) is. Two common cases:

- If the triangle RPD is right and DR is the hypotenuse (so the right angle is at P), use the Pythagorean theorem:
DP = sqrt(DR^2 − RP^2) = sqrt(16^2 − 12^2) = sqrt(256 − 144) = sqrt(112) = 4√7 ≈ 10.583.

- If the triangle is right and the right angle is at R (so DR and RP are the two legs), then
DP = sqrt(RP^2 + DR^2) = sqrt(12^2 + 16^2) = sqrt(144 + 256) = sqrt(400) = 20.

- If the triangle is not right-angled but you know an included angle θ, use the Law of Cosines:
DP^2 = DR^2 + RP^2 − 2·DR·RP·cos(θ).

Send the picture or the multiple-choice options and I’ll pick the correct setup.