Question

With reference to the diagram, what is cos A?

Answer 1

Answer:

cos(A)=sin(26.57°)=0.447

Step-by-step 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

$sin(C)=\frac{BD}{BC}$

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

$sin(C)=\frac{8}{17.89}=0.447$

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