The interior angle of four triangles are given below-TriangleInterior AnglesP85- 50-45-Q100- 55-25-R100- 45-35-S130- 30-20-Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys-

A triangle is said to be ill conditioned when angle is less than 30^∘ and more than 120^∘. So, triangle S is ill conditioned. For well conditioned of tri ...

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Standard VII

Mathematics

Right Angle Triangle

The interior ...

Question

The interior angle of four triangles are given below:

Triangle Interior Angles

P $85^{\circ}, 50^{\circ}, 45^{\circ}$

Q $100^{\circ}, 55^{\circ}, 25^{\circ}$

R $100^{\circ}, 45^{\circ}, 35^{\circ}$

S $130^{\circ}, 30^{\circ}, 20^{\circ}$

Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?

Both P and R

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Both Q and S

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Both P and S

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Both Q and R

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Solution

The correct option is B Both Q and S

A triangle is said to be ill-conditioned when angle is less $t h a n 30^{\circ} and more than 120^{\circ}$ .

So, triangle S is ill-conditioned.

For well-conditioned of triangulation two angle should not be almost equal.

So, only triangle Q or triangle R is ill-conditioned.
So, ill-conditioned S and Q or S and R. Option S and Q is given.
So option (b) is correct.

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Triangle	Interior Angles
P	$85^{\circ}, 50^{\circ}, 45^{\circ}$
Q	$100^{\circ}, 55^{\circ}, 25^{\circ}$
R	$100^{\circ}, 45^{\circ}, 35^{\circ}$
S	$130^{\circ}, 30^{\circ}, 20^{\circ}$

The interior angle of four triangles are given below: Triangle Interior Angles P 85∘,50∘,45∘ Q 100∘,55∘,25∘ R 100∘,45∘,35∘ S 130∘,30∘,20∘ Which of the triangles are ill-conditioned and should be avoided in Triangulation surveys?