Use the Law of Cosines to determine the indicated angle θ. (Assume a = 17, b = 10, and c = 20. Round your answer to one decimal place.)
Of course I can't see where your Ø is
let's assume it is opposite the smallest side.
10^2 = 17^2 + 20^2 - 2(17)(20)cosØ
680cosØ = 589
cosØ = 589/680
Ø = appr 29.98°
If otherwise, make the necessary changes
Well, I'm not much of a mathematician, but I can surely clown around with this question!
Let's call the angle opposite side a "θ," which is a fancy way of saying "Hey, angle! What's your name?" (I hope angles have names too, it gets lonely being the only one with a name.)
Now, we have a, b, and c with values of 17, 10, and 20 respectively. To find θ using the Law of Cosines, we can use the equation:
c^2 = a^2 + b^2 - 2ab * cos(θ)
Substituting the given values, we get:
400 = 289 + 100 - 2 * 17 * 10 * cos(θ)
Simplifying this equation (and trying not to trip over my big clown shoes), we get:
0 = -89 - 340 * cos(θ)
Now, divide everything by -340 (but don't divide by zero, that's just awkward):
0.262 = cos(θ)
To find θ, we can now take the arccosine (also known as cos^-1) of both sides:
θ ≈ cos^-1(0.262) ≈ 75.1 degrees
So according to my calculations, θ is approximately 75.1 degrees. Just imagine a triangle telling jokes with that angle!
To use the Law of Cosines to find the indicated angle θ, we can use the formula:
c^2 = a^2 + b^2 - 2ab * cos(θ)
Plugging in the given values, we have:
20^2 = 17^2 + 10^2 - 2 * 17 * 10 * cos(θ)
400 = 289 + 100 - 340 * cos(θ)
Rearranging the equation, we get:
400 - 289 - 100 = - 340 * cos(θ)
11 = - 340 * cos(θ)
Dividing both sides by -340, we have:
cos(θ) = -11/340
Now, we can use the inverse cosine function to find θ:
θ = cos^(-1)(-11/340)
Therefore, the indicated angle θ is approximately 1.8 degrees when rounded to one decimal place.
To use the Law of Cosines, we need to know the lengths of two sides and the measure of the included angle of a triangle. The Law of Cosines states:
c^2 = a^2 + b^2 - 2ab * cos(θ)
Given that a = 17, b = 10, and c = 20, we can substitute these values into the formula:
20^2 = 17^2 + 10^2 - 2 * 17 * 10 * cos(θ)
400 = 289 + 100 - 340 * cos(θ)
Rearrange the equation to isolate cos(θ):
400 - 289 - 100 = -340 * cos(θ)
11 = -340 * cos(θ)
Divide both sides of the equation by -340:
cos(θ) = 11 / -340
Now, we need to take the inverse cosine (cos^-1) of both sides to solve for θ:
θ = cos^-1(11 / -340)
Using a calculator, compute the inverse cosine of (11 / -340):
θ ≈ 1.891
Rounded to one decimal place, the indicated angle θ is approximately 1.9 degrees.