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In the figure, ABCD represents a large rectangular advertising board - NSC Mathematics - Question 7 - 2016 - Paper 2

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In the figure, ABCD represents a large rectangular advertising board. A surveyor, standing at the point P, is in the same horizontal plane as the bottom of the uprig... show full transcript

Worked Solution & Example Answer:In the figure, ABCD represents a large rectangular advertising board - NSC Mathematics - Question 7 - 2016 - Paper 2

Step 1

Calculate the length of AB.

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Answer

To find the length of AB, we will use the triangle PMA. Using the sine rule, we can calculate:

  • Since PM = 10 m and ∠PMA = 35°, we can use the cosine rule:

    AB=PM⋅sin⁡(∠PAM)AB = PM \cdot \sin(\angle PAM)

    First, we need to calculate angle PAM: ∠PAM=180°−(∠PMA+∠PMN)=180°−(35°+126.9°)=18.1°\angle PAM = 180° - (\angle PMA + \angle PMN) = 180° - (35° + 126.9°) = 18.1°

    Using that, we calculate:

    \approx 10 \cdot 0.310 = 3.10 ext{ m}$$ Therefore, the length of AB is approximately 3.10 m.

Step 2

Calculate how far the surveyor is from the board. (Length of PT)

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Answer

To find the length of PT, we will consider triangle PMT. Here, we have:

  • PM = 10 m,

  • MT = AB = 3.10 m,

  • Using Pythagorean theorem:

    PT=PM2−AB2PT = \sqrt{PM^2 - AB^2}

    Thus, we have:

    PT=102−3.102≈100−9.61≈90.39≈9.50extmPT = \sqrt{10^2 - 3.10^2} \approx \sqrt{100 - 9.61} \approx \sqrt{90.39} \approx 9.50 ext{ m}

    Therefore, the distance from the surveyor to the board (length of PT) is approximately 9.50 m.

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