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- anonymous

Challenge! Ready? Write the ratios for sin A and cos A. The triangle is not drawn to scale. http://assets.openstudy.com/updates/attachments/52f5130ae4b0512c88e57688-javo22-1391792928279-4568452232011112633am1351153605.png

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- anonymous

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- mathstudent55

Have you heard of SOHCAHTOA?

- anonymous

yes

- anonymous

Hint: it ends in a decimal

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- mathstudent55

Use the parts of SOHCAHTOA of the sine and the cosine.

- mathstudent55

I hate to tell you this, but it doesn't.

- anonymous

Oh?

- anonymous

Did I make a mistake then?

- DanJS

what is the opposite side of angle A

- anonymous

This type of triangle with the 90degrees and the 45degrees is a special type of triangle. Isosceles, i think. This means that the 7 side and the y side are always equal. the 45degrees and the unlabeled angle are the same, because the angles of the triangle add to 180. so, 180 - 90 -45 = 45. the unknown angle is 45degrees. Which also proves that the sides, 7 and y are the same length.
Then to find x, you can use Pathagorean's theorem. (spelling?) ... which says
C2=A2+B2
where C is the hypotenuse (across from the right angle), and A and B are the other sides.
So, for your problem,
x2=72+72=49+49=98
x=98−−√

- DanJS

an isosceles triangle has two sides of the same length, this one does not

- anonymous

Then Using SOHCAHTOA
hypotenuse = opposite / sin
x = 7 / sin45
x = 9.9
adjacent = opposite / tan
y = 7 / tan45
y = 7
Or using Pythagoras Theorem. A right angle triangle with two 45 degree angles means that two sides are the same. Therefore y also equals 7.
a^2 = b^2 + c^2 where a is the hypotenuse.
x^2 = 7^2 + 7^2
x^2 = 49 + 49
x^2 = 98
x = 9.9

- anonymous

I am redeeming myself....I guess I did it wrong sorry guys.

- DanJS

For a right triangle, the sin of the angle is the ratio of the opposite side divided by the hypotenuse side lengths

- DanJS

the sin of A would simply be 48/50

- anonymous

I see

- anonymous

I should have set up another challenge

- anonymous

I messed up, why???

- DanJS

oh, you are trying to challenge the panel maybe?, so you already know these things then

- anonymous

Yup.

- DanJS

oh, this is my fault, sorry

- DanJS

they need a new tab section, for these type questions

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