in triangle PQR, PQ=5.4, QR=3.6, and PR=6.2. to the nearest tenth, what is m<R?
cosine law ....
5.4^2 = 6.2^2 + 3.6^2 - 2(6.2)(3.6)cosR
cosR = 22.24/44.64
= .4982..
R = 60.1°
To find the measure of angle R in triangle PQR, we can use the Law of Cosines. The Law of Cosines states that in a triangle with sides a, b, and c, and angle C opposite side c, the following equation holds:
c^2 = a^2 + b^2 - 2ab * cos(C)
In this case, we know that side PQ has a length of 5.4, side QR has a length of 3.6, and side PR has a length of 6.2. We want to find angle R.
Applying the Law of Cosines, we have:
PR^2 = PQ^2 + QR^2 - 2 * PQ * QR * cos(R)
Plugging in the values we know:
6.2^2 = 5.4^2 + 3.6^2 - 2 * 5.4 * 3.6 * cos(R)
38.44 = 29.16 + 12.96 - 38.88 * cos(R)
Simplifying the equation, we get:
38.44 = 42.12 - 38.88 * cos(R)
Rearranging the equation to solve for cos(R), we have:
38.88 * cos(R) = 42.12 - 38.44
cos(R) = (42.12 - 38.44) / 38.88
cos(R) = 0.09
Now, we need to find the inverse cosine (also known as the arccosine) of 0.09 to find the measure of angle R. Using a calculator or a trigonometric table, we can find that the arccosine of 0.09 is approximately 84.3 degrees.
So, to the nearest tenth, m<R is approximately 84.3 degrees.