The value of angle A in the triangle is determined as 54.64⁰.
How to calculate the value of angle A?
The value of angle A is calculated by applying the following formula as shown below.
We will use cosine rule.
10² = 12² + 9² - 2(12 x 9) cos(A)
100 = 225 - 216 cos A
216 cos A = 225 - 100
216 cos A = 125
Divide both sides of the equation by 216;
cos A = 125 / 216
cos A = 0.5787
A = arc cos (0.5787)
A = 54.64⁰
Thus, the value of angle A is 54.64⁰