Can someone please show and explain how you got the answer for these please
1 answer:
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Answer:
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Step-by-step explanation:
<u>Triangle Solving</u>
If we had a triangle will its three sides of known length, we can solve for the rest of the parameters of the triangle, i.e. the area, perimeter and internal angles.
The three circles have diameters 900 m, 700 m and 600 m and are tangent to each other externally. The distances from their centers (where houses are located) are the sum of each pair of the radius of the circles. Thus, the sides of the triangle are
The internal angles can be computed by using the cosine's law
Where \alpha, \beta and \gamma are the opposite angles to x, y and z respectively. Solving for each one of them:
Similarly
The other angle is computed now
The area can be found by
Answer:
D. 7.8°
Step-by-step explanation:
There are many ways to work this problem. One is to subtract the angle of V from that of W:
∠V = arctan(2/-5) ≈ 158.20°
∠W = arctan(2/-8) ≈ 165.96°
Then ∠W -∠V = 165.96° -158.20° = 7.76° ≈ 7.8°
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Another is to divide W by V, since the quotient will have an angle that is the difference of their two angles.
(-8i +2j)/(-5i +2j) = (1/29)(44i +6j)
Then the angle of that is ...
arctan(6/44) ≈ 7.8°
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You can also divide the dot product by the product of the two magnitudes to find the cosine of the angle between the vectors.
(V•W)/(|V|·|W|) = 44/√(68·29) = cos(x)
x = arccos(0.990830168...) ≈ 7.8°
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A plot on graph paper will let you measure the angle with a protractor. You can obtain sufficient accuracy to choose between the offered answers.
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Your graphing calculator may have complex number functions that let you work directly with the angles of the vectors. (See second attachment. The calculator is in degrees mode.) Doing 2-dimensional vector calculations on a calculator may best be accomplished by treating them as complex numbers.
