Question

Consider right triangle ADEF below.EFDWhich expressions are equivalent to cos(ZE)?

Answer 1

The expressions equivalent to cos(∠E) are sin(∠F) and DE/EF

Which expression is equivalent to cos(∠E)?

From the question, we have the following parameters that can be used in our computation:

The right triangle

The value of cos(∠E) can be calculated using

cos(∠E) = Adjancent/Hypotenuse

Where, we have

Adjacent = DE and Hypotenuse = EF

Substitute the known values into the equation

cos(∠E) = DE/EF

Also,

cos(∠E) = sin(∠F) = DE/EF

Hence, the expressions equivalent to cos(∠E) are sin(∠F) and DE/EF

Question

Consider right triangle DEF below.

Which expressions are equivalent to cos(E)

DE/EF

tan(∠E)

sin(∠F)

cos(∠F)

Answer 2

The cosine ratio is given in the form:

`\cos\theta=(adj)/(hyp)`

From the triangle in the question, the different sides are labeled with respect to angle E as follows:

`\begin{gathered} hyp=EF \\ opp=DF \\ adj=DE \end{gathered}`

Therefore, the cosine ratio for ∠E will be:

`\cos(\angle E)=(DE)/(EF)`

ANSWER

`\begin{equation*} \cos(\angle E)=(DE)/(EF) \end{equation*}`