Application Of Triangles : 2

             A triangle is a three - sided polygon now and then called the trigon. Each triangle has three sides with three angles, a number of which may be the similar. The sides of a triangle are known particular name in the case of a right triangle, by means of the side opposed the right angle being word the hypotenuse and the other two sides being recognized as the legs. Every one triangles are convex and biocentrism.

 

               The sides opposed the angles A, B and C are after that labeled a, b, c by means of these symbols also representative the lengths of the sides.

 

Application of triangles in trigonometric functions:

 

We shall stand for the opposed side as “opp,” the adjacent side as “adj”, the hypotenuse as “hyp.”

  • sin(A) = opp / hyp

  • cos(A) =adj / hyp

  • tan(A) =opp / hyp = sin(A) / cos(A)

 

Example for Application of triangles:

 

Application of triangles - Example 1:

Find h.

 

Solution:

sin14° = h / 4.500

h =4.500 sin 14°

= 1.08 km

Application of triangles - Example 2:

Answer the triangle ABC, known that A = 37° and c = 18.

 

Solution:

To "answer" a triangle means to locate the unknown sides and angles. In this example, we require to locate a, b and angle B. Make a note of C = 90°.

We have

Sin 37° = a/c = a/18

So a = 18 sin 37° = 10.8

cos 37° = b/c = b/18

            So b = 18 cos 37° = 14.22

Angle B = 90° - 37° = 53°.

So a = 10.8, b = 14.22 and B = 53°.

 

 

 

Application of triangles - Example 3:

Let A = 38o, and a = 14.  Found b as well as c.

Solution:

Ratio between the identified side and the unidentified side through the identified side in the denominator. To establish while the trigonometric meaning of the identified angle represent that ratio, then equate the two.

To locate c, we explain c / 14 = csc 38o.  Therefore, c = 14 csc 38o = 14 (1.62) = 22.68

To locate b, we explain b / 14 = sec 38o.  Therefore, b = 14 sec 38o = 14 (0.84) = 11.76