Question

With reference to the diagram, what is cos A?

Answer 1

cos(A)=sin(26.57°)=0.447

Explanation:

we know that

In the right triangle ABC

The angle A and the angle C are complementary angles

so

∠A+∠C=90°

therefore

cos(A)=sin(C) -------> by complementary angles

we have

C=26.57°

sin(26.57°)= 0.447

Hence

cos(A)=sin(26.57°)=0.447

Alternative Method

In the right triangle BDC

`sin(C)=(BD)/(BC)`

Find BD applying Pythagoras Theorem

`BD^(2)=BC^(2) -DC^(2)`

substitute the values

`BD^(2)=17.89^(2) -16^(2)`

`BD^(2)=64.0521`

`BD=8\ units`

substitute the values

`sin(C)=(8)/(17.89)=0.447`

`cos(A)=sin(C)=0.447`