# Geometry

#### reggiwilliams

##### Junior Member
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

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
Where is the question?

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

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

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.

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.

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
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.

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.

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).