The area of land is 2.694 Km².
As per the above data given,
We need to find out the area of the land in the given figure.
According to given question,
it is stated that:
quadrilateral shaped piece of land with some measurements that is given in the figure.
BD²= AB²+ AD²-2AB. AD. cosA
(LAW OF COSINES-The law of cosines generalizes the Pythagorean theorem, which holds only for right triangles:c²= a² + b² − 2ab cos(C))
So, BD= 2.499kM.
[tex]\frac{BD}{sinc} = \frac{BC}{sin BDC}= \frac{CD}{ sinDBC}[/tex]
∠C=180°-47°-51°=82°
(Law of sines- In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles. a/sin A = b/sin B= c/sin C )
So, BC= 2.499/sin82°*sin47°= 1.846 Km
Now, further solving we get:
δΔABD= 1/2 AB.AD.sinA= 0.901
So, δΔBCD=1/2 BD.BC.sin ∠DBC= 1.793
so, δ= δ∠ABD+δ∠BCD= 2.694 Km²
Therefore, the area of land is 2.694 Km².
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