Question

Please solve (high points)

Answer 1

a = 13.24 m

Explanation:

Finding ∠A :

• ∠A + ∠B + ∠C = 180° (Angle Sum Property)
• ∠A = 180° - 48° - 54°
• ∠A = 180° - 102°
• ∠A = 78°

Applying the Law of Sines :

• a / sin78° = 10 / sin48°
• a / 0.98 = 10 / 0.74
• a = 13.51 x 0.98
• a = 13.24 m

Answer 2

13.2 m

Explanation:

The Law of Sines can be used to solve a triangle when angles and one side are known.

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setup

The angles of a triangle total 180°, so the missing angle A is ...

∠A = 180° -48° -54° = 78°

The Law of Sines tells us ...

a/sin(A) = b/sin(B)

a/sin(78°) = (10.0 m)/sin(48°)

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solution

Multiplying by sin(78°), we find ...

a = sin(78°)/sin(48°)×(10.0 m) ≈ 0.978148/0.743145×(10.0 m)

a = 13.1623 m

The length of side 'a' is approximately 13.2 meters.