Estimating Angles of a Box Diagonal

[kwal0203]

Homework Statement

Estimate to the nearest degree, the angles that a diagonal of a box with dimensions 10cm x 15cm x 25cm makes with the edges of the box.

Homework Equations

$cos\theta =\frac{u\cdot v}{\left \| u \right \|\left \| v \right \|}$

The Attempt at a Solution

For the angle between the diagonal vector and the edge with the 10cm side:

$u=(10,0,0)$
$v=(10,15,25)$

$cos\theta =\frac{(10,0,0)\cdot (10,15,25)}{\sqrt100\sqrt{100+225+625}}$
$cos\theta =\frac{100}{10\sqrt{950}}$

$cos\theta =\frac{10}{\sqrt{950}}$

Theta = ~71 degrees?

thanks, any help appreciated!

 

[Vargo]

Your denominator should be the product of the lengths of the two vectors. Vector u has length 10, right? Where's that? Vector v has length sqrt(950), why did you edit that to 100sqrt(850)?

 

[kwal0203]

Your denominator should be the product of the lengths of the two vectors. Vector u has length 10, right? Where's that? Vector v has length sqrt(950), why did you edit that to 100sqrt(850)?

Oh yeah, I had it right the first time. But if I do that then I can't carry out the next step.. how would you proceed in this question?

 

[kwal0203]

I edited it now, does it look right?

 

[Vargo]

Yeah, that looks right.