Given ABC with a = 23, b = 17, and c = 19, find mA . Round the cosine value to the nearest thousandth and answer to the nearest hundredth.
A simple application of the cosine law:
23^2 = 17^2 + 19^2 - 2(17)(19)cosA
solve for cosA, set your calculator to degrees, press 2nd F cos
(I anticipate an obtuse angle, since cosA will be negative.)
let me know what you get
You are looking for the size of the angle.
You got 4 ?????
from:
23^2 = 17^2 + 19^2 - 2(17)(19)cosA
529 = 289+361 - 646cosA
646cosA = 121
cosA = 121/646
angle A = appr 79.20° to the nearest hundredth
I was wrong to guess that the cosine would turn out negative
I got 4
To find the measure of angle A in the triangle ABC, we can use the Law of Cosines, which states that:
c^2 = a^2 + b^2 - 2ab * cos(A)
In this case, we are given that a = 23, b = 17, and c = 19. We need to find the measure of angle A, so we rearrange the equation to solve for cos(A):
cos(A) = (a^2 + b^2 - c^2) / (2ab)
Let's substitute the given values into the equation:
cos(A) = (23^2 + 17^2 - 19^2) / (2 * 23 * 17)
cos(A) = (529 + 289 - 361) / 782
cos(A) = 457 / 782
Now we can round the cosine value to the nearest thousandth:
cos(A) ≈ 0.584
Finally, we can find the measure of angle A by calculating the inverse cosine of 0.584:
mA ≈ cos^(-1)(0.584)
Using a calculator or math software, we find:
mA ≈ 54.6 degrees (rounded to the nearest hundredth)
Therefore, the measure of angle A in triangle ABC is approximately 54.6 degrees.