In a triangle X Y Z, ∠X=51^∘ ∠Y=67^∘ and Y Z=15.2 cm. Solve the triangle and find its area.

Name: Problem 27, Chapter 12: Higher Engineering Mathematics
Uploaded: 2021-12-26T16:31:53-08:00
Duration: 4 min 13 s
Channel: Mirza Aslam Beig
Description: In a triangle X Y Z, ∠X=51^∘ ∠Y=67^∘ and Y Z=15.2 cm. Solve the triangle and find its area.

step 1 The cochin is in triangle x y z angle x equal to 51 degree and angle y is equal to 67 degree and

In a triangle X Y Z, ∠X=51^∘ ∠Y=67^∘ and Y Z=15.2 cm. Solve...

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Key Concepts

Area of a Triangle Using Sine

The area of a triangle can be calculated using the formula (1/2)ab sin(C), where a and b are two sides and C is the included angle between them. This method is particularly useful when two sides and the included angle are known, providing a direct way to determine the triangle's area without needing additional information.

Triangle Angle Sum Property

This property states that the sum of the interior angles of any triangle is always 180 degrees. It is fundamental for determining a missing angle when the other two angles are known, ensuring that all elements of the triangle can be solved accurately.

Law of Sines

The Law of Sines relates the ratios of side lengths to the sines of their opposite angles in a triangle. This law is crucial when a triangle has known angles and at least one side length, allowing for the computation of unknown side lengths in an efficient manner.

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