A communications satellite is directly above the extension...

A communications satellite is directly above the extension of a line between receiving towers A and B. It is determined from radio signals that the angle of elevation from tower A is 88.9° and the angle of elevation from tower B is 86.6°. If A and B are 670 km apart, how far is the satellite from A? (Ignore the curvature of the earth.) distance = \boxed{} km (Round to the nearest thousand as needed.)

Transcript

00:01 This is problem number 35, in which it is given that a communications satellite is directly above the extension of a line between receiving towers a and b.

00:13 So, okay, it is determined from radio signals that the angle of elevation of the satellite from tower a is 89 .2 and b is 86 .5.

00:27 If a and b are 1 ,290 kilometers apart, how far is the satellite from a? so one thing for sure that if this is the line joining a and b, and this is extension line, so satellite has to be here somewhere.

00:51 If this is satellite, so there would be two points a and b.

01:03 Let it just okay it is being given that the angle of elevation from a is 89 .2 degrees so this has to be here 89 .2 degrees so a has to be here and b has to be here 86 .5 degree if a and b are 1 ,290 kilometers apart this is kilometers apart how far is satellite from a we need to find the value of a s okay okay no problem now s ab so we have to use cosine law or we can use sign law no problem but first we have to set in the value of this angle so that we could just move further so okay so value of angle that is angle s a b will be equal to 180 degree minus 89 .2 degrees so 180 minus 89 .2 degrees that will be be 90 .8 degrees 90 .8 degrees so this is 90 .8 degrees okay now this angle has to be equal to angle as b will be equal to 180 degree minus 86 .5 degree plus 90 .8 degrees as the sum of the angles of a triangle is always 180 degrees okay so this this will be 90 .8 plus 86 .5 minus 180 that is or 2 .7 degrees 2 .7 degrees so this angle is 2 .7 degrees now we'll be using a sign law sign law in triangle a b s which says sign of angle b by as equal to sign of angle s by a b because ab is a entity will be using this so sign of angle b we have already found angle b that is 86 .5 degree given 86 .5 degree divided by a s we have to find out equal to sign angle s that is this angle which is this this can also be written as angle s no problem 2 .7 degrees sine 2 .7 degrees divided by ab...

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