To measure a distance AB, a person runs 147.20 m from A to C, then turns 66.0° to face B, and runs 136.10 m to B. Calculate the distance AB, rounding the answer to two decimal places.
2007-06-04 17:16:01 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
There's a flaw in cattbarf's logic.
If you run from A to C, and then turn 66.0° to face B, the angle ACB is not 66.0° but 114.0°. The reason is that after running from A to C you are still facing away from A, not towards it. The angle between the continuation of AC and CB is 66°, and the angle ACB is supplementary to it.
The formula still applies, however:
c^2 = a^2 + b^2 - 2ab cos C
= 136.10^2 + 147.20^2 - 2(136.10)(147.20) cos 114.0°
= 56488
so c = √56488 = 237.7 m.
2007-06-04 17:27:49 · answer #1 · answered by Scarlet Manuka 7 · 1⤊ 0⤋
In the triangle ABC, angle C is actually 180 - 66 = 114.
The diagram will show that.
So AB^2 = 147.2^2 + 136.1^2 - 2*147.2*136.1*cos114
AB = 237.67 m
2007-06-04 17:29:28 · answer #2 · answered by Dr D 7 · 0⤊ 0⤋
Let a = 147.2 m
Let b = 136.1 m
Let C = 66 deg.
c^2 = a^2 + b^2 - 2 a b Cos C.
2007-06-04 17:19:57 · answer #3 · answered by cattbarf 7 · 0⤊ 1⤋