<p>I have this math problem for my math final. I can't get the correct answer.</p>
<p>The answer given is 11,000 km. </p>
<p>Here is the problem: A plane flies 500 kilometers with a bearing of N44W (North 44 degrees West) from B to C. The plane turns left and flies southwestly direction for 840 kilometers from C to A. How far is it from B to A? the answer is 11,000 km...anyone can tell me how to get to that answer?
Thanks a lot!!</p>
<p>i dind't get exactlly 11,000 i got apprx 1124.5 km, but it could be a result of some early rounding.</p>
<p>first draw a triangle ABC and label it accordingly with the given data</p>
<p>then use the sin rule to solve for angle A, you should get about 24.428 degress.</p>
<p>then use the rule of angles for triangles (all angles willadd up to 180 degress) to find C. (c can be one of two angles since sin of24.428 will correspond to two angles) however since you know the given answer is much larger that 500, it's safe to assume it's an obtuse angle. C should be about 111.58 degrees.</p>
<p>Use the sin rule again to figure out the length of AB.. which i calculated to be about 1124.5</p>
<p>it hink i did it right</p>
<p>11000 looks like it's way off. </p>
<p>I would think you would use the cosine rule here:</p>
<p>c^2 = a^2 + b^2 - 2ab cos(C)</p>
<p>where c = length of side opposite angle C,
b = length of side opposite angle B,
a = length of side opposite angle A</p>
<p>So, c^2 = 500^2 + 840^2 - 2(500)(840) cos(89 degrees)
= 250,000 + 705,600 - 840000 (0.017)
= 941320</p>
<p>c = sqrt(941320) = 970.2 km</p>
<p>right... cause your even farther off the answer is eleven thousand not one thousand lol i found that kinda funny</p>
<p>Chuck:</p>
<p>Sometimes the printed answers are wrong. Really.</p>
<p>Common sense tells us that the correct answer can be nowhere near 10000 km. If you travel 500 km from your starting point B, and then a further 840 km in any direction, what's the furthest you could be from B? It's 500 + 840 = 1340 km, assuming you continued in the same direction as the first leg of your journey. If you change direction, you will wind up being < 1340 km away from your starting point.</p>
<p>Can't be 11000. Optimizerdad is right.</p>
<p>no i know it just sounded really funny to me i did mean to sound criticizing just how it came off just struck me as somewhat funny</p>