What is the length to the nearest tenth of the hypotenuse DF of a right triangle DEF if FE is 13 units long and angle F is 34 degrees?

Answer 1

Without seeing the diagram your question (as originally written) was incomplete and impossible to answer.

If you had described your question (by rewriting it as I did) instead of blindly copying it, then the Answers community would have had all the necessary information to be able to answer your question and you would have got your homework done for you quicker. In fact, in rewriting the question you may actually have realised what was needed to be calculated and done it yourself - a very useful skill in being able to extract the required mathematics from the given information.

Anyway, what is now obvious from the rewritten question is you have is the cosine ratio:

cosine = adjacent/hypotenuse

→ cos F = FE / DF

→ DF = FE / cos F

As you didn't bother to give us the required information, I can't be bothered to fill in the numbers and calculate the required value - you can do that.

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What I was taught at pre-secondary school (some 40 odd years ago) to help remember the different trigonometric ratios:

In a right angle triangle there are three sides to an angle:

Opposite - the side opposite the angle

Adjacent - the side adjacent to the angle which is not the hypotenuse.

Hypotenuse - the side opposite the right angle

There are three ratios:

Tangent = Opposite / Adjacent

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

To remember them, use this nonsense rhyme:

Two Old Arabs

Soft Of Heart

Coshed Andy Hatchett

The initial letter of each word in each line gives the ratio:

Two Old Arabs → T = O / A → Tan = Opp / Adj

Soft Of Heart → S = O / H → Sin = Opp / Hyp

Coshed Andy Hatchett → C = A / H → Cos = Adj / Hyp

Answer 2

There is not enough information to answer the question. The question, as originally posted, did not specify that the triangle was right angled and you may not simply assume that DEF is right-angled. If you are willing to assume that then why not just assume that DF = 15.1 cm (or any number that you fancy) and be done with it!