Question

Two sides and an included angle of a triangular lot are measured as 2.56m.,3.54m, and 48.8° respectively.
Find the length of the third side
Find the angle opposite the 2.56m side.
Find the angle opposite the 3.54m side.
Find the area of the triangular lot.​

Answer 1

Answer:

sum of each 2.56 add other sudes

Answer 2

The third side is 2.67 cm

The opposite angle of side 2.56 is 46.05°

The opposite angle of side 3.54 is 90°

The area of the triangle is 3.4176 m²  

Given:

Two sides and an included angle of a triangular lot are measured as 2.56m, 3.54m, and 48.8° respectively  

To find:

Find the length of the third side

Find the angle opposite the 2.56m side.

Find the angle opposite the 3.54m side.

Find the area of the triangular lot.​  

Solution:

Formulas used:

Using the Law of Cosines, c² = a² + b² - 2ab cos(C)

Using the Law of Sines, a/sin(A) = b/sin(B) = c/sin(C)

Let a = 2.56, b = 3.54 and C = 48.8°

Using the Law of Cosines,

=> c² = (2.56)² + (3.54)² - 2(2.56)(3.54) cos(48.8)

=> c² = 7.15

=> c = 2.67    

Hence, the third side is 2.67 cm

Using the Law of Sines,

=> 2.56/sin(A) = 3.54/sin(B) = 2.67/sin(48.8)    

=> 2.56/sin(A) = 3.54/sin(B) = 3.54  

=>  2.56/sin(A) = 3.54  

=>  Sin (A) = 2.56/3.54 = 0.72

=> A = Sin⁻¹(0.72)

=> A = 46.05°  

Therefore,

The opposite angle of side 2.56 is 46.05°

=> 3.54/sin(B) = 3.54

=> Sin B = 3.54/3.54

=> B = Sin⁻¹(1)

=> B = 90°

Therefore,

The opposite angle of side 3.54 is 90°

 

Since one of the angles is 90° then the given triangle is a right-angled triangle

Area of right angle triangle = 1/2 (base × perpendicular)

= 1/2 (2.56)(2.67)

= 3.4176 m²  

Therefore,

The area of the triangle is 3.4176 m²  

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