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3. Use a proportion to find the distance across the water from C to D.
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From the figure, let the distance of point P from point A on line segment AB be x and let the angle opposite side a be M and the angle opposite side c be N.
Using pythagoras theorem,
and
Angle θ is given by
Given that a = 4 units, b = 5 units, and c = 9 units, thus
To maximixe angle θ, the differentiation of <span>θ with respect to x must be equal to zero.
i.e.
Given that x is a point on line segment AB, this means that x is a positive number less than 5.
Thus
Therefore, The distance from A of point P, so that </span>angle θ is maximum is 0.51 to two decimal places.
Using pythagoras theorem,
and
Angle θ is given by
Given that a = 4 units, b = 5 units, and c = 9 units, thus
To maximixe angle θ, the differentiation of <span>θ with respect to x must be equal to zero.
i.e.
Given that x is a point on line segment AB, this means that x is a positive number less than 5.
Thus
Therefore, The distance from A of point P, so that </span>angle θ is maximum is 0.51 to two decimal places.