Given m A =43 degrees ,a =6.9 and the information you noted above find c rounded to the hundredths place?
To find c, we can use the Law of Sines which states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.
Using the information provided, we have:
m A = 43 degrees
a = 6.9
Let's label the remaining angles and sides as follows:
m B = ?
m C = ?
b = ?
c = ?
Since the sum of angles in a triangle is 180 degrees, we can find angle B:
m A + m B + m C = 180
43 + m B + m C = 180
m B + m C = 180 - 43
m B + m C = 137
Since m A and m B are both acute angles, m C must also be acute. Therefore, m C = 137 - m B.
Applying the Law of Sines, we can express c in terms of angles and sides:
sin A / a = sin C / c
We know that sin A = sin 43° and a = 6.9, and we want to find c.
sin 43° / 6.9 = sin C / c
Next, we need to find angle C. Since the sum of angles in a triangle is 180 degrees, we can write:
m A + m B + m C = 180
43 + m B + (137 - m B) = 180
43 + 137 = 180
180 = 180
Therefore, angle C is right = 90 degrees.
Now, we can calculate c:
sin A / a = sin C / c
sin 43° / 6.9 = sin 90° / c
c = 6.9 * sin 90° / sin 43°
Using a calculator to evaluate the trigonometric functions, we find:
c ≈ 9.76 (rounded to two decimal places)
Therefore, c rounded to the hundredths place is 9.76.