Building a couch, could use some help

[Nmag]

Hey, picture attached. Hoping that this can be solved via sin cos and tan but it’s been to long for me to remember that.
Thanks in advance,
Nathan

 

[Dr.Peterson]

Hey, picture attached. Hoping that this can be solved via sin cos and tan but it’s been to long for me to remember that.
Thanks in advance,
NathanView attachment 28616

The sine of 80 degrees is defined as the ratio of the opposite side to the hypotenuse, which here is 16/a.

Does that refresh your mind? You need to solve for a. For b, use the cosine of 80 degrees.

 

[Otis]

Right-Triangle Trigonometry Video Example

?

 

[Nmag]

No offence guys I’m just a grocery store stocker. I asked because it’s been too long. Answers would be appreciated if at all possible. Trying to do something nice for my wife

 

[Dr.Peterson]

I took your statement to mean it's been too long to do it without a little help. We normally help people who want to learn something. But we can go further when needed.

But here's the work:

[imath]\sin(80^\circ) = \frac{16}{a}\\ a\sin(80^\circ) = 16\\ a = \frac{16}{\sin(80^\circ)} = \frac{16}{0.9848} \approx 16.25[/imath]​

​

[imath]\tan(80^\circ) = \frac{16}{b}\\ b\tan(80^\circ) = 16\\ b = \frac{16}{\tan(80^\circ)} = \frac{16}{5.67} \approx 2.82[/imath]​

Is that enough?

 

[Nmag]

I took your statement to mean it's been too long to do it without a little help. We normally help people who want to learn something. But we can go further when needed.

But here's the work:

[imath]\sin(80^\circ) = \frac{16}{a}\\ a\sin(80^\circ) = 16\\ a = \frac{16}{\sin(80^\circ)} = \frac{16}{0.9848} \approx 16.25[/imath]​

​

[imath]\tan(80^\circ) = \frac{16}{b}\\ b\tan(80^\circ) = 16\\ b = \frac{16}{\tan(80^\circ)} = \frac{16}{5.67} \approx 2.82[/imath]​

Is that enough?

Honestly no. I’m trying to figure out the optimal angle for a specific build and I read that you needed that size for a strong build on the back. 20 years ago yes I learnt and remembered but I can’t now. Pythagorean no problem but the trig escapes me

 

[Harry_the_cat]

So the angle you have marked is 80 degrees or not? What do you mean by optimal angle?

 

[Nmag]

I’m building this and a lounge chair and a small love seat myself. I found some basic instructions off of the web that I liked and I’ve extrapolated the picture but didn’t have full measurements. Just basically what I’ve drawn. Hoping to match what I’ve seen

 

[Harry_the_cat]

Dr P has given you the length of b in post #5. What else are you after?