Question

The included angles of three closed triangular traverses are given below

Triangle	Included angles
P	${240}^{\circ },{320}^{\circ },{340}^{\circ }$
Q	${240}^{\circ },{310}^{\circ },{350}^{\circ }$
R	${280}^{\circ },{310}^{\circ },{310}^{\circ }$

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

• A. R only
• B. P, Q and R
• C. P and Q
• D. P only

Answer 1

The correct option is C P and Q

The included angles are exterior angles the interior angles are tabulated below.

Triangle	Included angles
P	${120}^{\circ },{40}^{\circ },{20}^{\circ }$
Q	${120}^{\circ },{50}^{\circ },{10}^{\circ }$
R	${80}^{\circ },{50}^{\circ },{50}^{\circ }$

A triangle is said to be ill conditioned when interior angle is less than ${30}^{\circ }$ and more than ${120}^{\circ }$

$\therefore$ P and Q are ill conditioned.