How to Solve Angle Side Side Triangle Theorem

Definition:

ASS of triangle is determined by specifying two adjacent side lengths a and c of a triangle (with a < c), one acute angle A and the size of the third angle is calculated where, the total angle will equal 18° or II radians.

Example :

Find angle B,C and side b from angle A=5^o , side a=5 and side c=6

Given,

side a=5 side c=6 angle A=5^o

To Find,

Angle B, C and side b

Solution:

Substitute the given values in the respective formula,

Step 1:

Let us first find the value of a' side b' by substituting the values in the formula, b = (6 x cos 5^o) + ͩ(5 x 5) - (6 x 6 x sin 5 x sin 5) b = 5.825

Step 2:

Now, find the value of angle B. B = sin^-1((5.825 x sin 5)/5) B = sin^-1(.89244) B = 63.1837

Step 3:

Calculate the value of angle C. C = sin^-1((6 x sin 5)/5) C = sin^-1(.91925) C = 66.8163

Step 4:

Find the value of S. S = (5+5.825+6) / 2 S = 8.4125 Substitute the values in the area formula, Area = √ 8.4125 x (8.4125-5) x (8.4125-5.825) x (8.4125-6) Area = √179.231 Area = 13.3867

Step 5:

Now, find the value of perimeter. Perimeter = 5 + 5.825 + 6 Perimeter = 16.825