Answer:
Measure of angle B = 64.147°
Explanation:
Because we don't know whether this is a right triangle, we can find the measure of angle B using the Law of cosines
The law relates the lengths of the sides of a triangle to the cosine of one of its angles and has three forms
a^2 = b^2 + c^2 - 2bc * cos(A)
b^2 = a^2 + c^2 - 2ac * cos(B)
c^2 = b^2 + a^2 - 2ba * cos(C)
In the triangle, c is 11 units, b is 10 units, and angle A is 34°.
Step 1: Find the length of a:
Because the Law of Cosines requires all three sides, we must find side a's length.
We can use the first formula for the Law of Cosines and plug in 11 for c, 10 for b, and 34 for A, allowing us to solve for a:
1.1 Plug in values and simplify:
a^2 = 10^2 + 11^2 - 2(10)(11) * cos(34)
a^2 = 100 + 121 - 220 * cos(34)
a^2 = 38.61173404
1.2 Take the square root of both sides to solve for A
√(a^2) = √(38.61173404)
a = 6.213834085
Not rounding at this intermediate step in the problem will allow us to find the exact measure of angle B
Thus, a = 6.213834085 units.
Step 2: Find the measure of angle B:
Now we can use the Law of Cosines' second formula and plug in 11 for c, 10 for b, and 6.213834085 for a, allowing us to solve for B.
2.1 Plug in values and simplify
10^2 = 11^2 + 6.213834085^2 - 2(11)(6.213834085) * cos(B)
100 = 121 + 38.61173404 - 136.7043499 * cos(B)
100 = 159.611734 - 136.7043499 * cos(B)
2.2 Subtract 159.611734 from both sides:
(100 = 159.611734 - 136.7043499 * cos(B)) - 159.611734
-59.61173404 = -136.7043499 * cos(B)
2.3 Divide both sides by -136.7043499:
(-59.61173404 = -136.7043499 * cos(B)) / -136.7043499
0.4360631836 = cos(B)
2.4 Use cosine inverse to find the measure of angle B:
cos^-1 (0.4360631836) = B
64.14703487 = B
64.147 = B
Thus, the measure of angle B (rounded to the nearest thousandth) is 64.147°.