Geometry

[reggiwilliams]

Revising geometry at present and came across this question
Using Pythagoras calculated length 6m for PQ length 15m for QR.
As far as length of PR I used Cosine Rule to achieve an answer of 20.42.
Used SAS rule to find area of triangle PQR and got answer 22.5 sq metres but seems too small visually
Please let me have your views

 

[lev888]

Revising geometry at present and came across this question
Using Pythagoras calculated length 6m for PQ length 15m for QR.
As far as length of PR I used Cosine Rule to achieve an answer of 20.42.
Used SAS rule to find area of triangle PQR and got answer 22.5 sq metres but seems too small visually
Please let me have your views

Where is the question?

 

[reggiwilliams]

Question attached

Where is the question

 

[lev888]

Question attached

The solution looks good (didn't check the calculations). Why does the area seem too small?

 

[reggiwilliams]

The solution looks good (didn't check the calculations). Why does the area seem too small?

My calculation was1/2x6x15xSin150
Ie 22.5
When you consider area of PSQ is 24 just thought visually area of PQR would have been bigger but diagram probably not accurate

 

[Dr.Peterson]

My calculation was1/2x6x15xSin150
Ie 22.5
When you consider area of PSQ is 24 just thought visually area of PQR would have been bigger but diagram probably not accurate

Yes, it's the 150 degree angle that makes the difference. As a result, the altitude of the triangle with respect to QR as base is only 3, not 6.

Sketching the triangle in a plane would probably make this clearer.

 

[lev888]

My calculation was1/2x6x15xSin150
Ie 22.5
When you consider area of PSQ is 24 just thought visually area of PQR would have been bigger but diagram probably not accurate

It's good that you are checking whether the answer is reasonable. But in this case it's the diagram that's misleading you. The angle PQR is 150, but looks like it's 90. A better diagram would show the triangle PQR as one with a long base (PR) and a very short height, which, as you know, affects the area.

 

[jonah2.0]

Beer inspired diagram follows.

Revising geometry at present and came across this question
Using Pythagoras calculated length 6m for PQ length 15m for QR.
As far as length of PR I used Cosine Rule to achieve an answer of 20.42.
Used SAS rule to find area of triangle PQR and got answer 22.5 sq metres but seems too small visually
Please let me have your views

Revising or Revisiting?

My calculation was1/2x6x15xSin150
Ie 22.5
When you consider area of PSQ is 24 just thought visually area of PQR would have been bigger but diagram probably not accurate

It's all good.

reggiwilliams Geometry

www.desmos.com

 

[khansaheb]

Revising or Revisiting?

I think s/he meant reviewing. Back in middle/hS , we used to call "revising" - residual effect of colonial education system.

1/2x6x15xSin150

Suggest refrain from using " x " to indicate multiplication. Use " * " instead.

 

[The Highlander]

I think s/he meant reviewing. Back in middle/hS , we used to call "revising" - residual effect of colonial education system.

Suggest refrain from using " x " to indicate multiplication. Use " * " instead.

Or there is a 'multiplication' character available in the typefaces in the forum: "×"
Which could be used to produce: "½×6×15×Sin150".

Here's how it looks in all the available typefaces: × × × × × × × ×

PS: I've also replaced "1/2" with the single character "½" above.

For anyone that's interested, I've attached a little text file that I 'maintain' for the purpose of inserting 'special' characters (inter alia).
Anyone is welcome to download a copy for their own use.