Math SAT Question

<li><p>An area has bearings of N36degressW and N12degreesE. Two buildings are 20 miles from each other. The second building is directly east of the other building. A fire is moving toward the buildings. What is the distance of how fast the fire is moving?</p></li>
<li><p>A hiker climbs in a straight line. In one direction he goes 30 km and in the other direction he goes 45 km. In 2 hrs, the directions are 90 km apart. What is the measure of the trail in degrees?</p></li>
<li><p>Two planes leave the airport at the same time. Their speeds are 420 km/hr and 380 km/hr. The angle between them is 75 degrees. How far apart are they after 3 hours?</p></li>
</ol>

<p>I sent a private message with the answer to #3. I'll send the others in just a bit.</p>

<p>:)</p>

<ul>
<li>Liz</li>
</ul>

<p>Click on My Control Panel to see private messages.</p>

<p>A hiker travels 30 km in a straight line. He then travels an additional 45 km. In 2 hrs, they are 90 km apart. What is the bearing in degrees? I'll make 30 km vertical and 45 km horizontal. The 2 hrs begins after the hiker has traveled the 30 km in one direction and 45 in another.</p>

<p>I can't remember the exact question, but I think that the wording said that the fire was 10 miles away from the building</p>

<h1>3. Two planes leave the airport at the same time. Their speeds are 420 km/hr and 380 km/hr. The angle between them is 75 degrees. How far apart are they after 3 hours?</h1>

<p>I used law of cosines, 75 degrees is the included angle. After 3 hours, the lengths of the sides are 1140 and 1260. c is the distance between the planes
c^2 = (1140)^2 + (1260)^2 - 2<em>1140</em>1260*cos75
c = 1,464.1</p>

<p>Correct? #1 I have no idea how to do, I'm trying #2 again... it seems to me like you need more info for #1.</p>

<ol>
<li>sqrt(1260^2+1140^2-2(1260*1140)cos(1.30899694))=1464.1259</li>
</ol>

<p>For the second question, it sounds like you can use the law of cosines, but it doesn't work out.</p>

<p>Actually, #2 is an impossible triangle, because the length of any two sides is not greater than the length of the third side:</p>

<p>45+30 = 75 </p>

<p>75 < 90.</p>

<p>No solution.</p>

<p>yeah, i tried it too but chalked it up to a mistake and didn't bother anymore. i got arccos(-1.933) or something, so... not possible. maybe you copied it wrong?</p>