word problem ?s...dealing with trigonometry.

I

itchycontrolyou

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Jan 9, 2006
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The shorter diagonal of a rhombus with a 70 deg. angle is 124 cm long. HOw long is the longer diagonal?

Huh? I know diagonals, but longer and shorter? Implying the whole diagonal and half of the whole diagonal? Where do I start?
so confuseeedddd... :shock: :?
 
draw a picture ...

the 70 degree vertex angle will be the smaller angle and
the larger vertex angle of the rhombus will be 110 degrees.

the diagonals of a rhombus bisect each other and their respective vertex angles.

Draw in the diagonals ... what you end up with is four congruent right triangles {each (1/4) of the rhombus}, any one of which with angles of 35 degrees and 55 degrees. The side of each right triangle adjacent to the 55 degree angle and opposite the 35 degree angle will be 62 cm (half the shorter diagonal).

Use your trig ratios to solve for the other leg of the right triangle, which will be half the length of the longer diagonal.
 
itchycontrolyou said:
how did you get 35 && 55 for the angle measures?
Click to expand...

You are given that one angle of the rhombus has a measure of 70 degrees. You should know that the opposite angles of any parallelogram (and that would include a rhombus) are equal, and that the consecutive angles of any parallelogram are supplementary.

So, if one angle has a measure of 70, so does the opposite angle. The remaining two angles must each have a measure of 110, so that any pair of consecutive angles adds up to 180.

Now, Skeeter pointed out that the diagonals of a rhombus bisect each other AND the angles of the rhombus. When you bisect an angle of 70 degrees, you get two 35-degree angles. When you bisect an angle of 110 degrees, you get two 55-degree angles....

I hope that helps you.
 
ok...now that i look back at my drawing, i drew the picture wrong. let me go back....i'll keep you posted. thank you for the help!! :D
 
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