Given with b = 5, c = 32, and m(angle)A=40° , find a. Round the cosine value to the nearest thousandth and answer to the nearest hundredth
use the law of cosines:
a^2 = b^2 + c^2 - 2bc cosA
I got
20.33 is it okay?
Nope. You should check to see whether an answer you get makes sense.
Try to draw a triangle with a base of 32, with the other sides 5 and 20.33
It can't be done. Even stretching the other two sides out flat, they are not long enough to form a triangle. You know that you need c < a+b
Too bad you didn't show how you got that value. Try again.
To find side a of the triangle, we can use the cosine law. The cosine law states that for any triangle with sides a, b, c, and angle A opposite to side a:
a^2 = b^2 + c^2 − (2 * b * c * cos(A))
In this case, we have b = 5, c = 32, and A = 40°. Now we can substitute these values into the cosine law equation:
a^2 = 5^2 + 32^2 − (2 * 5 * 32 * cos(40°))
Next, we can calculate the cosine of 40° using a scientific calculator or online tool. The cosine of 40° is approximately 0.766044. Now we can substitute this value into the equation:
a^2 = 25 + 1024 − (2 * 5 * 32 * 0.766044)
Simplifying further:
a^2 = 25 + 1024 − (320 * 0.766044)
a^2 = 25 + 1024 − 245.29248
a^2 = 803.70752
Finally, to find a, we need to take the square root of both sides:
a = √803.70752
a ≈ 28.357
Rounding the cosine value to the nearest thousandth (0.766) and rounding the answer to the nearest hundredth, we have:
a ≈ 28.36