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Shortest Distance Triangle (4iii)

I am fine with part i) and ii) (having the answers being 1.55km and 124° respectively). It is just part iii) I am struggling with; I know that it is the height of the triangle from angle C to AB that I have to go about doing. A walkthrough would be greatly appreciated.
IMG_6470.JPG502.6KB
Reply 1
Avatar for Zacken
Zacken
22
Original post by Earl_Earl
I am fine with part i) and ii) (having the answers being 1.55km and 124° respectively). It is just part iii) I am struggling with; I know that it is the height of the triangle from angle C to AB that I have to go about doing. A walkthrough would be greatly appreciated.


Yes, indeed. The shortest distance to a point from a line is the line drawn from the point C that intersects the line AB perpendicularly. This should make intuitive sense. Once that's done, you know have a right-angled trianngle. You know the hypotenuse and you know one of the angles. Hence sin(angle) = opposite/hypotenuse. This then lets you find the opposite which is what you want.

As attached below:



The red line is the distance you want, it is also the 'opposite' to the angle 40 degrees and the blue line is your hypoteneuse.
Reply 2
Avatar for Zacken
Zacken
22
I need to learn how to spell hypothenuse. #IlliterateMathmos
Reply 3
Avatar for Earl_Earl
Earl_Earl
OP
1
Original post by Zacken
I need to learn how to spell hypothenuse. #IlliterateMathmos


Thank you
Reply 4
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Zacken
22
Original post by Earl_Earl
Thank you


No problem.
Reply 5
Avatar for Notnek
Notnek
21
Original post by Zacken
I need to learn how to spell hypothenuse. #IlliterateMathmos

Hypothenuse is pretty much obsolete in English speaking countries. Hypotenuse is the common spelling nowadays.
Reply 6
Avatar for Zacken
Zacken
22
Original post by notnek
Hypothenuse is pretty much obsolete in English speaking countries. Hypotenuse is the common spelling nowadays.


Oh god, I spelt it wrong again. :rofl:

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