Answer:
A = 3/5
Step-by-step explanation:
At the outset, the question doesn't give us a figure to refer to nor does it tell us if this is a right angled triangle. However we observe that both sin A and tan A have the numbers 3, 4 and 5. We recognize this to be consistent with 3-4-5 standard right angled triangle.
Hence we can guess that it is probably a right angled triangle, but we should do the following to confirm:
Knowning that for a right angled triangle,
sin A = opposite / hypotenuse = 4/5
tan A = opposite / adjacent = 4/3
From this we can surmise that
Opposite = 4
hypotenuse = 5
adjacent = 3
Assemble the triangle to see if this works (see attached). We can futher verify that 3-4-5 works using the Pythagorean theorem.
Now that we have determined that the triangle is a 3-4-5 right angled triangle,
cos A = adjacent / hypotenuse = 3/5
