In the diagram. AC = 11cm, BC = 5.5cm and B^AC = 25°.It is given that A^BC is an obtuse angle. Calculate A^BC.
Not familiar with the notation A^BC for an angle
The usual notation is angle ABC, where B would be the vertex of the angle and the containing sides would be AB and BC
Explain your notation.
To calculate angle A^BC, we can use the trigonometric relationship known as the Law of Cosines. This law states that in a triangle with sides a, b, and c, and the opposite angles A, B, and C, the following equation holds true:
c² = a² + b² - 2ab * cos(C)
In this case, we have angle A^BC (opposite to side AC) and sides AC and BC. We want to find angle A^BC, so let's assign the following values:
AC = 11 cm
BC = 5.5 cm
A^BC = x (the angle we want to find)
Plugging in the values into the Law of Cosines equation, we get:
(5.5)² = (11)² + (5.5)² - 2(11)(5.5) * cos(x)
30.25 = 121 + 30.25 - 121 * cos(x)
Simplifying:
30.25 = 30.25 - 121 * cos(x)
121 * cos(x) = 121
cos(x) = 121 / 121
cos(x) = 1
To find the angle, we can use the inverse cosine function (also known as arccos) on both sides of the equation:
x = arccos(1)
Using a calculator, we find that arccos(1) is 0 degrees.
Therefore, the value of angle A^BC is 0 degrees.