Why is this result different? (calculating the sides of a triangle)

In summary, this person plugged their angle into the surface area formula for a triangle, and got a different result than what was given in the textbook. However, the two solutions are the same up to the decimal point.
  • #1
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Homework Statement
Given the surface area of the right triangle = 22 cm^2 and one of his angles is 38°40'.
Calculate his other sides.
Relevant Equations
A=ab/2, tan(38°40')=b/a
so basically, here is a photo from the textbook(in attachments) and I'll write here how I did it. In my opinion, results should have been the same, but for some reason, they differ. So, if anyone can tell me what I am doing wrong I would appreciate it since I can't find mistakes caused by wrong calculations then it must be something conceptual that does not apply here, which is weird.
This is how I did it:
##A=\frac{ab}{2}## I wrote one side(b) using angle and the other side(a) like this: tan(38°40')=b/a --> 0.8a=b and then I plugged that in the formula for the surface of the triangle, after which I got b= 7.42. Which is the same as in solutions, this second part is what confuses me.

To calculate a, I just plugged b in 0.8a=b and got a=9.28. But in the textbook, b is plugged back in the formula for triangle surface and they got a = 5.93. After that our hypotenuses differ as well(obviously).
pf123.jpg
 
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  • #2
Callmelucky said:
here is a photo
Where?
 
  • #3
phinds said:
Where?
in attachments, don't know why you can't see it, it's shown to me
 

Attachments

  • pf123.jpg
    pf123.jpg
    14.4 KB · Views: 61
  • #4
I've edited your attachment to make it full size.

Callmelucky said:
This is how I did it:
##A=\frac{ab}{2}## I wrote one side(b) using angle and the other side(a) like this: tan(38°40')=b/a --> 0.8a=b and then I plugged that in the formula for the surface of the triangle, after which I got b= 7.42. Which is the same as in solutions, this second part is what confuses me.

To calculate a, I just plugged b in 0.8a=b and got a=9.28. But in the textbook, b is plugged back in the formula for triangle surface and they got a = 5.93.
Since your answer for b agreed with the one in your textbook, just use it and the given area to solve for a.
##22 = \frac 1 2 a \cdot 7.42 \Rightarrow 7.42 a = 22##
Doing this, the value I got for a, rounded to two decimal places was 5.93.
 
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  • #5
Callmelucky said:
Homework Statement:: Given the surface area of the right triangle = 22 cm^2 and one of his angles is 38°40'.
Calculate his other sides.
Relevant Equations:: A=ab/2, tan(38°40')=b/a

so basically, here is a photo from the textbook(in attachments) and I'll write here how I did it. In my opinion, results should have been the same, but for some reason, they differ. So, if anyone can tell me what I am doing wrong I would appreciate it since I can't find mistakes caused by wrong calculations then it must be something conceptual that does not apply here, which is weird.
This is how I did it:
##A=\frac{ab}{2}## I wrote one side(b) using angle and the other side(a) like this: tan(38°40')=b/a --> 0.8a=b and then I plugged that in the formula for the surface of the triangle, after which I got b= 7.42. Which is the same as in solutions, this second part is what confuses me.

To calculate a, I just plugged b in 0.8a=b and got a=9.28. But in the textbook, b is plugged back in the formula for triangle surface and they got a = 5.93. After that our hypotenuses differ as well(obviously).
Textbook solution:
pf123-jpg.jpg


You said:
I wrote one side(b) using angle and the other side(a) like this: tan(38°40')=b/a --> 0.8a=b and then I plugged that in the formula for the surface of the triangle, after which I got b= 7.42.
Show the details of what you plugged into ##\displaystyle A=\frac{ab}{2}## to get ##b##.

(I suspect that you actually found that ##a=7.42## cm.)
 
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  • #6
Mark44 said:
I've edited your attachment to make it full size.Since your answer for b agreed with the one in your textbook, just use it and the given area to solve for a.
##22 = \frac 1 2 a \cdot 7.42 \Rightarrow 7.42 a = 22##
Doing this, the value I got for a, rounded to two decimal places was 5.93.
I got that too, but the way I solved it first time is also correct, that is why I posted question
 
  • #7
SammyS said:
Textbook solution:
View attachment 323523

You said:

Show the details of what you plugged into ##\displaystyle A=\frac{ab}{2}## to get ##b##.

(I suspect that you actually found that ##a=7.42## cm.)
I found my mistake. What an idiot I am. I plugged the value of (a) instead of (b), and instead of multiplying with 0.8 I divided it by 0.8, therefore got the wrong result. I am sorry for waisting everybody's time. Thank you.
 

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