Answer:
a = 11.9883 in
Explanation:
Sides:
a = 5.6 in
b = 11.9883 in
c = 10.6 in
Angles:
A = 27.8476 °
B = 90 °
C = 62.1524 °
Other:
P = 28.1883 in
s = 14.0942 in
K = 29.68 in2
r = 2.10584 in
R = 5.99416 in
SAS is Side, Angle, Side
Given the size of 2 sides (c and a) and the size of the angle B that is in between those 2 sides, you can calculate the sizes of the remaining 1 side and 2 angles. Use The Law of Cosines to solve the remaining side.
Law of Cosines
If a, b and c are the lengths of the legs of a triangle opposite to the angles A, B and C respectively; then the law of cosines states:
a^2 = c^2 + b^2 - 2bc cos A, solving for cos A, cos A = ( b^2 + c^2 - a^2 ) / 2bc
b^2 = a^2 + c^2 - 2ca cos B, solving for cos B, cos B = ( c^2 + a^2 - b^2 ) / 2ca
c^2 = b^2 + a^2 - 2ab cos C, solving for cos C, cos C = ( a^2 + b^2 - c^2 ) / 2ab
Solving, for example, for an angle, A = cos^-1 [ ( b^2 + c^2 - a^2 ) / 2bc ]