Final answer:
To find the measure nearest 10th of a degree in the given triangle, we can use the law of cosines. By substituting the known values into the formula and solving for the angle, we find that the measure is approximately 71.1 degrees.
Step-by-step explanation:
To find the measure nearest 10th of a degree, we can use the law of cosines. The law of cosines states that the square of one side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of the lengths of those sides multiplied by the cosine of the included angle.
In this case, we know the lengths of sides r, s, and t, so we can substitute those values into the formula and solve for the angle.
Using the law of cosines, we have:
t^2 = r^2 + s^2 - 2rs*cos(t)
Substituting the given values, we have:
840^2 = 440^2 + 850^2 - 2*440*850*cos(t)
Simplifying and solving for cos(t), we get:
cos(t) = (440^2 + 850^2 - 840^2) / (2*440*850)
Plugging in the values, we have:
cos(t) = 0.310
Now, we can use the inverse cosine function to find the angle t:
t = cos^(-1)(0.310)
Using a calculator, we find that t is approximately 71.1 degrees.
Therefore, the measure nearest 10th of a degree is 71.1 degrees.