sine: side BC is 5, side CA is 12, need to find sine of A

[tamiatha]

sine = opposite side divided by hypoteneuse
what if i don't know the measurement of the hypoteneuse
it is a right triangle
side BC is 5
side CA is 12
i need to fine the sine of A
thank you

 

[stapel]

it is a right triangle
side BC is 5
side CA is 12
i need to fine the sine of A

Since "CA" is a side, then "A" is a point (that is, a vertex). You cannot take the sine of a point. Sorry!

what if i don't know the measurement of the hypoteneuse

The steps one takes to solve a triangle will vary with the information provided. For instance, if one had the lengths of the two legs and one needed the length of the hypotenuse, one would apply the Pythagorean Theorem. Other situations, of course, would require other tools and methods. :wink:

 

[Aladdin]

Applying pythagores theorem you find the hypotenous , and Sin(A)=opp/hyp

 

[tamiatha]

c^2 = a^2 + b^2
c^2 = 17^2
sin = opp/hyp
289/144 = 2.0069
have i done it correctly now
thank you for your help

 

[mmm4444bot]

… c^2 = 17^2 …

Whoops! We need to follow the Order of Operations.

We do exponentiation before we do addition.

You added 12 + 5 first, to get (12 + 5)^2 = 17^2; that's wrong because (12 + 5)^2 is not the same order as 12^2 + 5^2.

Square the numbers first, then add the results.

12^2 + 5^2 = 144 + 25

Now, continue …

AND, be careful that you divide the opposite length by the length of the hypotenuse. Your work looks like you put your wrong value for the hypotenuse in the numerator and the length opposite angle A in the denominator. That's backwards.

sin(A) = Opposite/Hypotenuse

Also, a few words about notation for triangle sides and angles. It is standard to use capital letters to represent the angles, and lower case letters to represent the side lengths.

Label vertices using A, B, and C. Label sides using a, b, and c.

Therefore, you could label the vertex at the right angle as C. The hypotenuse is opposite angle C, so label the hypotenuse as c.

The angle at vertex A has measure A, and the side opposite this angle has length a.

The remaining vertex is B, so the angle there has measure B, and the side opposite has length b.

Now we can talk about any triangle ABC using the symbols A, B, and C to describe the angles and symbols a, b, and c to describe the sides.

In your exercise, I think we have C = 90 degrees, a = 12, and b = 5. Is that correct? The side opposite angle A has length 12?

If so, then we could write the ratio Opposite/Hypotenuse as follows.

sin(A) = a/c

Thank you for showing your work. Please continue to do so, if you would like more help with this exercise.

 

[tamiatha]

thank yu for explaining so clearly
my answer is .8571
correct?

 

[mmm4444bot]

… my answer is .8571

correct?

Your answer does not look correct, to me, but I'm still not sure that I understand the exercise because you did not answer my question.

I previously asked you if the length opposite angle A is 12. Is it?

Also, you did not show your work, so I do not know what value you're using for the length of the hypotenuse.

Please answer my question, and show your work.

 

[tamiatha]

yes it is 12
i will show my work tomorow
i have run out of time tonight
thank you

 

[mmm4444bot]

Thank you for that information.

It looks, to me, like you're either using 14 (which is an incorrect value) for the length of the hypotenuse or you pressed a wrong digit on your calculator when trying to divide by the correct value.

Double-check your arithmetic.