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We are given the following sketch of a quadrilateral shaped piece of land with some measurements. Find the area of the land. Give your answer as a decimal rounded to three significant figures. Do not include the unit with your answer.

Sagot :

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.

For more such questions on Area :

https://brainly.com/question/29025813

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