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Problem 87 Hard Difficulty

Diagonal of a cube: A cubical box has a diagonal measure of 35 cm. (a) Find the dimensions of the box and (b) the angle $\theta$ that the diagonal makes at the lower corner of the box.
FIGURE CANT COPY

Answer

a. approx. $20.2 \mathrm{cm}$ for each side
b. approx. $35.3^{\circ}$

Discussion

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Top Algebra Educators
GH
Grace H.

Numerade Educator

Catherine R.

Missouri State University

Caleb E.

Baylor University

Kristen K.

University of Michigan - Ann Arbor

Video Transcript

for this question, we're asked to do two things. First of all, we need to find I mentions of our Q. Newest. Please find the angle. Faith, huh? So to start off with, we can't notice that a triangle is being formed right here. It's under start off with. We noticed that this section over here, one set of our triangle is just outside the box. That just be X. We know that this side of the triangle is equal to 35 7 years and we do not know what this triangle is equal to. So you start off with let's try to figure out that said Trunk. Also in that this side will be access while so if we actually pull up this triangle, let's read. Ross is a little bit more to scale. He knows that this is X. This is X. This isn't unknown. So why don't we call this unknown? Why? So we know that using by Sawyer and them know that Why? So we know that X squared plus X squared is equal to y squared. So we know that two x squared to go to y squared saying that why is equal to score with a two x squared. So why is equal to X skirt too? Now that we know what why is we could try to tackle our big triangle so we draw their big triangle. We noticed that our hope on Inis is 35. Why is exported to our side is X so we try software it. So we know that X squared plus X squared two scored is equal to 35 squared. This is over a So we know that X squared plus two x squared. It's equal to 35 squared. So in the three x squared see what your 35 squared an X squared people to 35 squared over three. So you know X is equal to 35 for Route three, which is equal to 35. Route three number three which we in So then if we wants an approximate so 35 3/3 is our approximate answer or our exact answer But we want to find our approx. My answer. It is approximately equal to 20 point to one centimeters. So there's are two answers to printing for looking for exact or approximate. So they're dimensions of our Cube. So for party were asked to find angle data and so we actually already happened. Information we need. So once again, we tried during on a triangle. It's just 35 centimeters. No, that we now know that this is 35 Route 3/3. So that then we know that this side over here is 35 route three times. You're too. It was just to get us 35 Route 6/3. And this is state over here. And so we can use our sign to try Figure out Seda. So you know that sign of Seda is equal to 35 with 3/3 over 35 which is equal to Cynthia is equal to Well, if we think about the 35 on the bottom so we can rewrite this as 35 times three. So I would just guess what, 3/3. So, based off of that information, you say that he was this sign in verse 3/3 soon a data people to approximately 35.26 degrees

Westview High School
Top Algebra Educators
GH
Grace H.

Numerade Educator

Catherine R.

Missouri State University

Caleb E.

Baylor University

Kristen K.

University of Michigan - Ann Arbor