Answer:
A. The length of the third side is approximately 5 feet.
B. A = , B =
and C =
.
Step-by-step explanation:
Let the triangle be ABC. Given two sides and an included angle, let us apply the cosine rule to determine the third length.
A. Let side a = 6 feet and c = 3 feet, thus;
=
+
- 2ac Cos B
= +
- 2(6 x 3) Cos
= 36 + 9 - 36 x 0.5
= 45 - 18
= 27
b =
= 5.1962
b = 5.2 feet
b ≅ 5 feet
The length of the third side is approximately 5 feet.
B. Given that B = , then let us apply the Sine rule to determined the measure of A.
=
So that,
=
Sin A =
Sin A = 0.99923
A = 0.99923
= 87.75
A ≅
Since the sum of angle in a triangle = .
Then,
A + B + C =
+
+ C =
+ C =
C = -
=
C =
Thus,
A = , B =
and C =
.