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Find the lengths of all three sides of each triangle. SEE EXAMPLE 3 20. E 4x +12 F 20 3x + 5 ​

1 Answer

3 votes

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.

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