Question 156675: for each triangle, two sides are given. What is the third side?
15 ft, 33 ft
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! i don't believe you have enough information to find the third side.
you would need an angle between them to fix their position relative to each other.
otherwise you have an infinite number of possible 3d sides.
once you have an angle between them you can use trigonometry to solve for the length of the 3d side unless you just want to lay them out and measure.
in your example, you have 2 sides of 15 and 30 feet. they are connected on one side and are free to swing around at any angles relative to each other unless you fix the angle between them.
once you fix the angle, the rest is calculation or measurement.
for example, assuming you fix the angle between them at 30 degrees.
now you can either measure or use trigonometry to solve for the length of the 3d side.
using trigonometry, i was able to determine that the 3d side length was 18.5897 feet in length.
how i did it follows:
AB is 15 feet in length.
AC is 30 feet in length.
fix the angle at 30 degrees between them at point A.
for drawing purposes you can approximate 30 degrees which will be good enough.
drop a perpendiular from point B (other end of line AB) to AC. it will intersect line AC at point D forming line segments AD and DC.
this forms right triangles ADB and CDB.
now use trig formulas to get some distances which will allow you to find the length of BC (your 3d leg).
angle DAB is 30 degrees because you constructed it that way (it's the angle between your first 2 line segments AB and AC.
i used the cosine of angle DAB which is 30 degrees to get the length of line segment AD which came out to be 12.9903... feet.
since line AC is 30 feet and line segment AD is 12.9903... feet i was able to get the length of line segment DC which was 30 feet - 12.9903... feet.
so line segment DC came out to be 17.0096... feet. (AD and DC are both part of line segment AC).
still working with triangle ADB i was able to get the length of line segment BD (the perpendicular that was dropped from point B to intersect with line AC at D) by using the sine of angle DAB.
the line segment BD came out to be 7.5 feet.
now i moved over to triangle CDB to find angle DCB since that was still unknown.
i used tangent of angle formula to find angle DCB since i knew the adjacent side length (line DC) and the opposite side length (line DB.
once i found the angle of DCB which turned out to be 23.7939... degrees, i was then able to find the length of BC by using the sine formula for angle DCB.
i double checked my figures and used pythagoreum theorem to make sure i did the calculations correctly and everything checked out.
bottom line:
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knowing the 2 line segments isn't enough.
you need the angle between them as well.
draw a picture if you wish to follow this. keep it reasonable within scale.
line AB is 15 feet in length.
line AC is 30 feet in length.
30 degrees angle between them at point A (angle formed is CAB).
30 degrees was used for example purposes only. angle you want is the one you will be working with.
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