Answer check please

[12345678]

Hi, I was wondering if somebody could check my answer. the question asked to find the obtuse angle, labelled x. So using sine rule, I did Sin30/70 (used cm)= sinx/100. therefore sinx=sin30/70 * 100. this came out at 0.714285. I then used sin-1(0.714285), and got an answer of 45.6. However, the markscheme says it is 134, and I know 45.6 is not obtuse. know where I have gone wrong?

 

[DrPhil]

Hi, I was wondering if somebody could check my answer. the question asked to find the obtuse angle, labelled x. So using sine rule, I did Sin30/70 (used cm)= sinx/100. therefore sinx=sin30/70 * 100. this came out at 0.714285. I then used sin-1(0.714285), and got an answer of 45.6. However, the markscheme says it is 134, and I know 45.6 is not obtuse. know where I have gone wrong?

If you use a calculator for arcsin, it will give you the answer in the 1st (or 4th if negative) quadrant only. You have to use what you know about sines in the 2nd quadrant.

 

[12345678]

If you use a calculator for arcsin, it will give you the answer in the 1st (or 4th if negative) quadrant only. You have to use what you know about sines in the 2nd quadrant.

Sorry, I'm only doing GCSE and I don't understand you. Are you saying my calculator is on the wrong setting?

 

[HallsofIvy]

Sorry, I'm only doing GCSE and I don't understand you. Are you saying my calculator is on the wrong setting?

sin(0)= 0 and, as x increases, sin(x) increases to 1 at sin(90)= 1, then goes back down to 0. So there will be two different values, between 0 and [itex]\pi[/itex] (0 and 180 degrees) that give the same sine value. For example $\displaystyle sin(\pi/4)= \sqrt{2}/2= sin(2\pi/2)$ (or $\displaystyle sin(45)= \sqrt{2}/2= sin(135)$. If you use your calculator to determine the arcsine, it can only give you one of those answers and the convention is that it gives you the value between 0 and $\displaystyle \pi/2$ (between 0 and 90 degrees). You have to use what additional information you have to determine if the angle you want is between 0 and $\displaystyle \pi/2$ (0 and 90 degrees) or between $\displaystyle \pi/2$ to $\displaystyle \pi$ (90 to 180 degrees).

 

[wjm11]

Hi, I was wondering if somebody could check my answer. the question asked to find the obtuse angle, labelled x. So using sine rule, I did Sin30/70 (used cm)= sinx/100. therefore sinx=sin30/70 * 100. this came out at 0.714285. I then used sin-1(0.714285), and got an answer of 45.6. However, the markscheme says it is 134, and I know 45.6 is not obtuse. know where I have gone wrong?

Your calculator is on the right setting.
Your calculator will only give you an acute angle answer, even if you are looking for an obtuse angle.
Your calculations are fine as far as you went, but you needed one last step; you needed to subtract your calculator answer from 180 degrees to get the correct answer.
Here is why. If you are given triangle information in the order: angle, side1, side2 (30 degrees, 100cm, 70cm) AND side2 < side1 (70cm < 100 cm), there are two possible triangles that can be constructed from this information. You have solved for an angle in the OTHER triangle than the one pictured.

The "big picture": you need to identify those cases in which two triangles can be constructed from the given information. You need to understand which of those triangles your calculator answer applies to.

If you can construct the "other" triangle I am referring to, you will discover the 45.6 degree angle that you arrived at.

Hope that helps.