The angle measure of angle A is 50.5 degrees.
The image shows a triangle ABC, with angle A being the unknown angle. The sides AB and BC are given to be 11 cm and 9 cm respectively. The angle B is given to be 38 degrees.
To find the size of angle A, we can use the Law of Sines. The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is the same for all three sides.
In this case, we can write the Law of Sines as follows:
AB / sin(A) = BC / sin(B)
Substituting in the given values, we get:
11 / sin(A) = 9 / sin(38)
Cross-multiplying and solving for sin(A), we get:
sin(A) = (11 * sin(38)) / 9
sin(A) = 0.7908
Taking the inverse sine of both sides, we get:
A = arcsin(0.7908)
A = 50.5 degrees
Therefore, the size of angle A is 50.5 degrees.