Answer:
Explanation:
Relationship to calculate triangle lengths
Let's consider a triangle whose sides are a, b, and c and angles
�
α,
�
β,
�
γ. The sides of the triangle are related to each other with the cosine law:
cos
�
=
�
2
+
�
2
−
�
2
2
×
�
×
�
cos
�
=
−
�
2
+
�
2
+
�
2
2
×
�
×
�
cos
�
=
�
2
−
�
2
+
�
2
2
×
�
×
�
cosα=
2×b×c
b
2
+c
2
−a
2
cosβ=
2×a×c
−b
2
+c
2
+a
2
cosγ=
2×b×a
b
2
−c
2
+a
2
Using the triangle length calculator
Let ⊿ABC be a right-angled triangle having sides, a and b, forming the right angle, equal to 3 and 4, respectively.
To find the missing side length:
Fill in the angle,
�
=
90
°
γ=90°.
Enter the length of side,
�
=
3
a=3.
Input the length of side,
�
=
4
b=4.
Using the triangle length calculator:
cos
�
=
�
2
−
�
2
+
�
2
2
×
�
×
�
cos
90
°
=
4
2
−
�
2
+
3
2
2
×
4
×
3
0
=
16
−
�
2
+
9
12
�
2
=
16
+
9
�
=
16
+
9
=
5
cosγ
cos90°
0
c
2
c
=
2×b×a
b
2
−c
2
+a
2
=
2×4×3
4
2
−c
2
+3
2
=
12
16−c
2
+9
=16+9
=
16+9
=5
The third side of the triangle is 5.