Trigonometry helps to calculate the correct angle for the triangular support. Also trigonometry envisages the builders to correctly layout a curved structure.

**Application to Triangle**

Much of architecture and
engineering relies on triangular support on any structure where stability is
desired. Trigonometry helps to calculate the correct angle for the triangular
support. Also trigonometry envisages the builders to correctly layout a curved
structure. For a right triangle, any two information with atleast one side say *SS, SA* are sufficient to find the
remaining elements of the triangle. But, to find the solution of an oblique
triangle we need three elements with atleast one side. If any three elements
with atleast one side of a triangle are given, then the Law of Sines, the Law
of Cosines, the Projection formula can be used to find the other three
elements.

**Working Rule:**

Â·
In a right triangle, two sides determine the third side via the
Pythagorean theorem and one acute angle determine the other by using the fact
that acute angles in a right triangle are complementary.

Â·
If all the sides of a triangle are given, then we can use either
cosine formula or half-angle formula to calculate all the angles of the
triangle.

Â·
If any two angles and any one of the sides opposite to given
angles are given, then we can use sine formula to calculate the other sides.

Â·
If any two sides of a triangle and the included angle are given,
we cannot use the Law of sines; but then we can use the law of cosines to
calculate other side and other angles of the triangle. In this case we have a
unique triangle.

Â·
All methods of solving an oblique triangle require that the
length of atleast one side must be provided.

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11th Mathematics : UNIT 3 : Trigonometry : Application to Triangle | Solved Example Problems, Exercise | Mathematics

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