Final answer:
To find the largest angle in a triangle with sides of length 4, 5, and 7 units, you can use the Law of Cosines. Applying this formula, the largest angle is approximately 88.6 degrees.
Step-by-step explanation:
To find the largest angle in a triangle with sides of length 4, 5, and 7 units, we can use the Law of Cosines. This law states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the lengths of those sides and the cosine of the included angle. In this case, the largest angle is opposite the longest side.
Let's call the longest side c and the other two sides a and b. Using the formula for the Law of Cosines, we have c^2 = a^2 + b^2 - 2ab*cos(C), where C is the angle opposite side c.
Plugging in the values, we have 7^2 = 4^2 + 5^2 - 2*4*5*cos(C). Solving for cos(C), we get cos(C) = 0.058. Taking the inverse cosine of this value, we find that the angle C is approximately 88.6 degrees.