trig

[swimmer3]

The two equal sides of an isosceles triangle are each 36cm. If the base measures 30cm, find the height and the measure of the two equal angles.

I was able to solve the problem completely but of the answer choices I was not quite sure because they did not match up completely:
either a.The height is 33cm; the angles are 65 dgrees. or b. The height is 33cm; the angles are 67 degrees.

I came up with the angles being 66.4 degrees which would be 66 degrees using the sin method and the other being 24.6 degrees which would be 25.6 degrees. So I was thinking the answer would have to be a?

 

[mmm4444bot]

… I came up with the angles being 66.4 degrees … using the [sine] method …

The correct answer is (a).

You did not show any work, so I have no way to determine how you arrived at the incorrect angle measure 66.4 degrees.

The angle is 65.37 degrees (rounded to two places).

 

[wjm11]

The two equal sides of an isosceles triangle are each 36cm. If the base measures 30cm, find the height and the measure of the two equal angles.

I was able to solve the problem completely but of the answer choices I was not quite sure because they did not match up completely:
either a.The height is 33cm; the angles are 65 dgrees. or b. The height is 33cm; the angles are 67 degrees.

I came up with the angles being 66.4 degrees which would be 66 degrees using the sin method and the other being 24.6 degrees which would be 25.6 degrees. So I was thinking the answer would have to be a?

Your problem is with roundoff error. Yes, the height is ~33cm, but do not use 33 in your angle calculation.

If you want to use the height in your angle calculation, you must use something more accurate – say 32.726, for example. Better yet, use half the base (15cm) and the 36cm hypotenuse along with the inverse cosine function.

The angle is ~65.38 degrees. The “answer” is A.

 

[mmm4444bot]

Actually, I think I do know how you arrived at 66.44 degrees.

You used the rounded measurement of 33 for the height, instead of 32.7261… .

Do not round-off intermediate results! Otherwise, you risk introducing "round-off error".

Just let the calculator carry all of its digits, as you progress through the calculations, and save any rounding for the very end.

 

[mmm4444bot]

… The angle is 65.37 degrees (rounded to two places).

Speaking of round-off error …

Bill is correct. 65.38 degrees (rounded to two places).