Find the indicated angle è. (Use either the Law of Sines or the Law of Cosines, as appropriate. Assume a = 95 and c = 137(angle B=38). Round your answer to two decimal places.)
Your given information is of the format SAS , so it requires the cosine law to find c
c^2 = 95^2 + 137^2 - 2(95)(137)cos 38°
...
c = 85.335
I would now find angle A using the sine law, then the third angle is easy.
i got that far too but i cant figure out the angle C!!!!
Just noticed that I was actually finding b, not c
(c was given)
No harm done here.
let's find angle A by the sine law
sinA/a = sinB/b
sinA/95 = sin 38/85.335
sinA = .685...
A = 43.27
then angle C = 180-38-43.27 = 97.73° or appr 98°
The problem with the sine law is that we run into the "ambiguous case".
since the sine is positive in I and in II, when we take the inverse sine, we often cannot tell which angle to use.
In this case, since the largest angle is always opposite the largest side, angle C must be the largest.
So I try to avoid finding that angle by the sine law, and I found angle A instead.
Since any triangle could have only ONE obtuse angle, by finding one of the two smaller angles we avoid that problem
thank you!!!
i dot geht thhis werlk? cahn sumwone elp meh?
I didn't know this, and I feel like I was cheated by my geomtery teacher.I feel like I should have known this I am a math professor with a Ph.D. but I'm comforted to hear that a lot of other people didn't know about it, either.
To find the indicated angle è, we can use the Law of Sines. The Law of Sines states that in any triangle:
sin(A) / a = sin(B) / b = sin(C) / c
Using this formula, we can write:
sin(A) / a = sin(B) / b
Given the values of angle B (38 degrees), side c (137), and side a (95), we can substitute these values into the formula.
sin(A) / 95 = sin(38) / 137
To find angle A, we can solve for sin(A) by cross-multiplying:
sin(A) = (sin(38) / 137) * 95
Now, to find angle A, we need to take the inverse sine (also known as arcsin) of both sides:
A = arcsin((sin(38) / 137) * 95)
Calculating this expression will give us the measure of angle A. Remember to round your answer to two decimal places as specified in the question.