Question

In ∆ABC, if sin A = 4/5 and tan A = 4/3 , then what is cos A?

A. 3/5

B. 4/5

C. 3/4

D. 5/3

Answer 1

A

Explanation:

Answer 2

A = 3/5

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