Question

PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!

Find the cosine of ∠F.

Write your answer as an integer or as a decimal rounded to the nearest hundredth.


cos(F) =

Answer 1

Answer:

0.51

Step-by-step explanation:

Use knowledge of trigonometric ratios to find cos(F).

Remember:

sin(x) = opposite/hypotenuse

cos(x) = adjacent/hypotenuse

tan(x) = opposite/adjacent

In this case, we're dealing with cosine, so let's use the cosine formula.

cos(F) = adjacent/hypotenuse

When you look at the diagram, you can see that the you are only given opposite and hypotenuse, so we still need the length of the adjacent side.

Since this is a right triangle, we can use the Pythagorean Theorem, $a^2+b^2=c^2$, to find the length of the adjacent side.

So $a^2$ + 56² = 65².

Solve for a.

$a^2$ + 3136 = 4225

$a^2$ = 4225 - 3136 = 1089

a = √1089 = 33

Now that we know the length of the adjacent side, we can go back and use the cosine formula.

cos(F) = adjacent/hypotenuse

cos(F) = 33/65 ≈ 0.51

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Answer 2

Answer:

Step-by-step explanation:

$DF=\sqrt{65^2-56^2} =\sqrt{(65+56)(65-56)} =\sqrt{9*121} =3*11=33\\cos (F)=\frac{33}{65} \approx 0.51$