Maths trig question

16

Zara is an engineer. She is building a wall, which needs to be supported as it is built. The ground is perfectly horizontal, the wall is perfectly vertical and the support is a straight steel beam. For the wall to be safe, the angle between the beam and the ground must be less than 55°.

If the support beam is 12m long and the end of the support is 3.5m away from the base of the wall, is the wall safely supported?

OK, so would I have to use Trig to work out the angle btween the beam and the ground, and see if this is more or less than 55' to see if the wall is safely supported?

Sorry, this is a really wordy question, so i'm having trouble processing what I would have to do.

Reply 1

TypicalNerd

18

Original post by Blackrose06

Zara is an engineer. She is building a wall, which needs to be supported as it is built. The ground is perfectly horizontal, the wall is perfectly vertical and the support is a straight steel beam. For the wall to be safe, the angle between the beam and the ground must be less than 55°.

If the support beam is 12m long and the end of the support is 3.5m away from the base of the wall, is the wall safely supported?

OK, so would I have to use Trig to work out the angle btween the beam and the ground, and see if this is more or less than 55' to see if the wall is safely supported?

Sorry, this is a really wordy question, so i'm having trouble processing what I would have to do.

You need to draw a right-angled triangle.

One face of the triangle is the wall, the base of the triangle is the floor and the hypotenuse must be the beam, since the floor is assumed to be flat and it says the beam is at an angle to the floor.

Can you now label the known sides of this triangle and use SOH CAH TOA to find the angle?

Reply 2

Blackrose06

OP

16

So the beam is the Hypotenuse, so would be H, and the floor is the Adjacent, so is A. so I would need to use CAH to work out the angle.

Reply 3

Blackrose06

OP

16

Ok, i've done the working out.
cos(x)= 3.5/15=0.2916...
cos-1(0.2916...)=73.0427...= 73.04'
Because the angle is more than 55', the wall is not safe.
I think i've done that correctly.

Reply 4

TypicalNerd

18

I believe that is correct.

The question is worded rather poorly imo, as theoretically speaking the “end of the support” could be referring to where the beam meets the wall or the point where it touches the floor.

(edited 1 year ago)

Reply 5

Blackrose06

OP

16

Original post by TypicalNerd

I believe that is correct.

The question is worded rather poorly imo, as theoretically speaking the “end of the support” could be referring to where the beam meets the wall or the point where it touches the floor.

OK thank you. I know the maths, just lots of words over complicate things, and confuse me.

Reply 6

TypicalNerd

18

Original post by Blackrose06

OK thank you. I know the maths, just lots of words over complicate things, and confuse me.

I was much the same.

I’d honestly recommend having a highlighter in the exams or simply just underlining key information so it’s easier to keep track of.

I also found drawing diagrams (particularly in mechanics and with graphical problems in pure maths) to help a lot, too.

Maths trig question

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