Question

HELP PLEASE!!!!
Two points P and Q on level ground are on opposite sides of a building. To find the distance between the points, a surveyor chooses a point R that is a = 331 feet from P and c = 458 feet from Q and then determines that angle PRQ has measure α = 39°50' (see the figure). Approximate the distance between P and Q. (Round your answer to the nearest whole number.)

Answer 1

use the law of cosines:
PQ^2 = a^2 + b^2 - 2*a*b*cos (theta), where a and b are the sides given and theta is the given angle.

Answer 2

The law of cosines is the general form of the pythagorean theorem. You can use it even if you don't have a right angle because it relates the angle you have to the sides.

Answer 3

Can you please help to solve that? I keep getting the wrong answer

Answer 4

\[=\sqrt{331^{2}+458^{2}-2(331)(458)\cos(39.833)}\]
\[=\sqrt{86497.345}\]
\[=294.1\]

Answer 5

\[PQ ^{2} = 331^{2} + 458^{2} -2 \times 331 \times 458 \times \cos 39.5\]
\[PQ ^{2} = 85371.5\]
\[PQ = 292.184\]

Answer 6

50 minutes = 50/60 degrees

Answer 7

Hmmm.../my webassign says that's wrong((

Answer 8

haha did you round to nearest whole number ?

Answer 9

Oh 294 is correct answer. Thank you))

Answer 10

Oh. I didn't know about minutes. When I was learning geometry in my country we never used them. Thank you for telling me. Sorry about that Nazyma. I hope I didn't confuse you.

Answer 11

It's ok. You really helped. Thanks))