Die prent en die diagram hieronder toon 'n hyskraan PQR wat 'n boks vanaf punt M tot punt R optel. PQ en MR is loodrig op die grondvlak, MP, sodanig dat PQRMC in dieselfde vertikale vlak is. T is 'n punt op MR. PQ = 8 m; PQR = 114° en QPR = 49° 6.1 Bepaal die lengte van PR. 6.2 Skryf die grootte van R P ~ M neer. 6.3 Voltooi die volgende verhouding met betrekking tot ΔR P M: sin R P M = ... As TR = 5 m, bepaal MT.

NSC Technical Mathematics Euclidean Geometry: Die prent en die diagram hierond

Die prent en die diagram hieronder toon 'n hyskraan PQR wat 'n boks vanaf punt M tot punt R optel - NSC Technical Mathematics - Question 6 - 2023 - Paper 2

Question 6

Die prent en die diagram hieronder toon 'n hyskraan PQR wat 'n boks vanaf punt M tot punt R optel. PQ en MR is loodrig op die grondvlak, MP, sodanig dat PQRMC in die... show full transcript

Worked Solution & Example Answer:Die prent en die diagram hieronder toon 'n hyskraan PQR wat 'n boks vanaf punt M tot punt R optel - NSC Technical Mathematics - Question 6 - 2023 - Paper 2

Step 1

Bepaal die lengte van PR.

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Answer

To find the length of PR, we can apply the Law of Sines in triangle PQR. The Law states that:

$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$

Here, we can label the sides opposite to the angles as follows:

Let PR = a
Let PQ = 8 m (given)
Angle PQR = 114° (given)
Angle QPR = 49° (given)

We can find the third angle, QRP: $QRP = 180° - PQR - QPR = 180° - 114° - 49° = 17°$

Using the Law of Sines: $\frac{PR}{\sin(49°)} = \frac{8}{\sin(17°)}$

Therefore, $PR = \frac{8 \cdot \sin(49°)}{\sin(17°)}$

Calculating this gives: $PR \approx 24.34 \text{ m}$

Step 2

Skryf die grootte van R P ~ M neer.

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Answer

The angle R P ~ M can be determined using the triangle properties. Given that MR is vertical:

$R P ~ M = 180° - (PQR + QPR) = 180° - 114° - 49° = 17°$

Step 3

Voltooi die volgende verhouding met betrekking tot ΔR P M: sin R P M = ...

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Answer

To complete the equation, we can apply the Sine Rule for triangle RPM:

$\frac{PM}{sin R P M} = \frac{RP}{sin(17°)}$

This leads us to: $sin R P M = \frac{PM \cdot sin(17°)}{RP}$

Step 4

As TR = 5 m, bepaal MT.

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Answer

To find MT, note that triangle MRT is a right triangle:

MR = TR + MT Using Pythagorean theorem:

$MT = MR - TR$

From earlier, if MR can be calculated from the angles, we would find MT accordingly. Final calculation pending previous values.

Die prent en die diagram hieronder toon 'n hyskraan PQR wat 'n boks vanaf punt M tot punt R optel - NSC Technical Mathematics - Question 6 - 2023 - Paper 2

Worked Solution & Example Answer:Die prent en die diagram hieronder toon 'n hyskraan PQR wat 'n boks vanaf punt M tot punt R optel - NSC Technical Mathematics - Question 6 - 2023 - Paper 2

Bepaal die lengte van PR.

Skryf die grootte van R P ~ M neer.

Voltooi die volgende verhouding met betrekking tot ΔR P M: sin R P M = ...

As TR = 5 m, bepaal MT.

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