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

[Callmelucky]

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).

 

[phinds]

here is a photo

Where?

 

[Callmelucky]

Where?

in attachments, don't know why you can't see it, it's shown to me

 

[Mark44]

I've edited your attachment to make it full size.

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.

 

[SammyS]

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:

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.)

 

[Callmelucky]

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

 

[Callmelucky]

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.