am not getting my answes right for th 4th time ne1 help? its on trignometry sine rule?

Question

a triangle with angle 122degrees is opposite to a length of 14cm.
angle feta degrees is opposite to length x. And the other side is 10cm. Find x and feta.

Please show your working out. thnx.

Answer 1

Took me 4 tries to get this right... :( I think....

Thanks to spikypig below for catching my mistake...I think I did arccos instead of arcsin.

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This problem is pretty "cheesy".

122° + "feta" + angle3 = 180°
angle3 = 180° - 122° - feta

sine rule:

sin(122°)/14 = sin(feta)/x = sin(180° - 122° - feta)/10

Using the first and last ones:

sin(122°)/14 = sin(180° - 122° - feta)/10
10sin(122°)/14 = sin(58° - feta)
sin(58° - feta) = 0.6057
58° - feta = 37.3°
feta = 20.7°

Then:

sin(122°)/14 = sin(20.7°)/x
x = 14sin(20.7°)/sin(122°)
x = 5.84 cm

Sorry...I really screwed this up the first time...

Answer 2

Pick a point marked "A" in the middle of a piece of paper and draw a point. Draw a 2-inch line going to the right and mark it x
draw a 2-ish-inch line at an angle of 122 degrees from horizontal (it will go up and left from the point) and mark the angle you just created 122. mark the line you just drew "10". Connect the ends of the two lines and mark the new line 14. I think this is the triangle you are describing.
Now, extend the "x" line to the left in a straight line, past point "A".
Drop a perpendicular line from the top of the triangle to the extended line and mark the vertical line "y". Mark the horizontal extension of the "x" line "a".
Draw the new angle formed on the bottom, which is 58 degrees (180 - 122).
Now you have a right triangle, and a = 10*cos(58 degrees).
You also have y = 10*sin(58 degrees)
Does that make sense?
Now you have a right angle where you know y and 14, so (a+x)^2 + y^2 = 14^2. You can solve for (a+x), which means you can solve for "a".

There are a number of ways to solve for the angle feta. One is to use the knowledge of a+x and y to compute the sum of "feta and q" where q is the angle between the "10" line and the "y" line. The angle q is 90 - 58, or 32 degrees.

Answer 3

Ok start with a diagram. All the angles in a triangle add up to 180 degrees. 122 is the known angle so the other 2 must sum to 58. The unknown angle opposite x is theta, so call the other one phi.
phi = 58 - theta and theta = 58 - phi. Using sine rule:

Sin(122) / 14 = Sin(phi) / 10 which solves for phi, which is used to find theta.
theta = 20.7 (rounded)

Using the sine rule with this angle
Sin(theta) / x = Sin(122) / 14
Which can be solved for x to get
x = 5.84cm

I think this is correct.

The answer given by the first man gives arcsin(0.605) incorrectly
Arcsin(0.605) = 37.3, not 52.7 as shown in the first answer, but his method used is correct.

Answer 4

I can see why your having problems!!
If your working with the law of sines, sines only work on angles less than 90 (well, 90 works but you get 1 then) !! I think you'd have you the law of cosines. Unless, you drop the height from the exterior and make a right triangle, then find angles there
Ok, the law of sines says that
sine of angle a / side A = sine of angle b / Side B
or whatever angles and opposite side works. Also you could flip it where you divide the side by the sine of the angle.
side A / sine of angle a = side B / sine of angle b
Anyways, you make some equations, and hopefully things can work out. My best guess is use the law of cosines, sorry, i can't really solve with it on my computer though :-)

Answer 5

x^2 + 10^2 - 2(x)(10) Cos122 = 14^2

Solve for x (neglect negative value)

Then solve for
Sin (feta) / x = Sin(122) / 14