Die diagram hieronder stel twee waarnemers by P en Q voor wat ewe ver van punt R is - NSC Technical Mathematics - Question 6 - 2022 - Paper 2

We can use the Law of Sines to find RQ.
Using the angle from step 6.1:

$RQ = \frac{481,1}{\sin{33,9°}} \cdot \sin{112,2°}$

Calculating gives:

$RQ = 289,81 m$

We can find h using the tangent function from angle ∠SQR:

$\tan{23,5°} = \frac{h}{289,81}$

Rearranging for h gives:

$h = 289,81 \cdot \tan{23,5°}$

Calculating gives us:

$h \approx 126 m$

To find the area of triangle QPR, we can use the formula:

$Area = \frac{1}{2} \cdot base \cdot height$

Using base RQ and height h, we have:

$Area = \frac{1}{2} \cdot 481,1 \cdot 289,81 \cdot \sin{112°}$

Calculating this results in:

$Area \approx 382,88 m^2$