Sigh…why is this not coming out? I have a problem where i am given the two lengths of a triangle and an angle. In this case, a = 6.8, c =2.4, with angle beta= 10.5°. I find length b easily with b= 4.5, but the remaining two angles aren’t matching with the textbook. Using the law of cosine, angle alpha came out to 159.8°, but the book came out with 163.9°. What gives?
This might just be a rounding error. Try keeping a few more digits of your answer for b when you’re solving for alpha, and see if it helps.
I use trig everyday and I cant remember jack cept’ how to set a sine bar…
I thought u bisected into two right triangles…180 - 10.5 - 10.5 = 159 … but my calcualor sucks.
I will second MikeS. Your value for b is off just enough, I suspect, to account for the discrepancy. Remember (or learn that cos changes rather slowly at angles that are near 0 or 180, so that a small change in length might result in a large change in the angle. Using the rule of sines, I came up with 163.87.
A quick calculation by me got b=4.4617, which is far enough from 4.5 to cause a few degree difference on the angles.
If you have 3 lengths and an angle, try using the sine rule to get the other angles? The one that says angle/length = angle/length
I second everyone who says it’s a rounding error, but I also note that calculating the length of b is not necessarily the easiest way to get the answer. Ease is in the eye of the beholder, mind you, but I assume what you did was calculate the length of b from a, c, and beta, using the law of cosines, and then the angle alpha from a, b, and c using the law of cosines again.
It might be easier to calculate alpha via its tangent rather than its cosine: b * sin(alpha) = a * sin(beta) [laying the triangle with c as its base, this is the height of the opposite corner], and b * cos(a) + a * cos(beta) = c [here we are summing the (signed) horizontal displacements of the corner opposite c from the other two corners]. Combining these, we have that tan(alpha) = sin(alpha)/cos(alpha) = (a * sin(beta))/(c - a * cos(beta)). [The bs cancel out]. Plugging in a, beta, and c gives you tan(alpha) = -0.28911876…; taking the inverse tangent of this (within the range from 0 to 180 degrees) gives you 163.874426… degrees, as the book says.
This triangle calculator agrees.
yes, it was a rounding error. I wasn’t including enough numbers when I attempted to find the arc cosine of the number.
on a side note, is it possible to use the law of sine with this problem?
A 40 ft. wide house has a roof with a 6-12 pitch(the roof rises 6 ft for a run of 12 ft). The owner plans a 14 ft wide addition that will have a 3-12 pitch to its roof. Find the lengths.
I figured you could only use the law of cosine since there are no angles for you to work from.