The angle of the triangular plot at which the surveyor stands is 83°
A triangle is a shape with three sides and three angles. From the information given, the sides of the three angles are different, we can say the triangle is a scalene triangle since no sides are equal.
To determine the angle of the triangular plot at which the surveyor stands, we need to use the cosine formula.
Given that:
Let's assume that the angle at which the surveyor stands is ∠A, then:
[tex]\mathbf{a^2= b^2+c^2-2 bc \times Cos A}[/tex]
Making cos A the subject, we have:
[tex]\mathbf{cos \ A = \dfrac{ b^2+c^2-a^2}{2bc}}[/tex]
[tex]\mathbf{cos \ A = \dfrac{ 250^2+200^2-300^2}{2(250 \times 200)}}[/tex]
[tex]\mathbf{cos \ A = 0.125}[/tex]
A = cos⁻¹ (0.125) ≅ 83°
Learn more about calculating the angles of a triangle here:
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