Question

the diagram represents a triangular car park pqs and a building rq of height 70 metres.
t is a point on ps such that \\(pt : ts = 5 : 3\\)
\\(ps = 144\\) metres, \\(q\hat{p}t = 63^{\circ}\\) and \\(s\hat{t}q = 114^{\circ}\\)

(a) show that \\(qt = 103\\) metres rounded to the nearest whole number.

(b) determine the angle of elevation of r from s. round off your final answer to the nearest whole number.

Explanation:

Calculate the lengths of PT and TS

$$
LATEXBLOCK0
$$

Apply the Law of Cosines to find QT

$$
LATEXBLOCK1
$$

Calculate the angle of elevation of R from S

$$
LATEXBLOCK2
$$

Answer:

Question (a)

Using the Sine Rule in \(\triangle PQT\):

$$ \hat{PTQ} = 180^\circ - 114^\circ = 66^\circ $$

$$ \hat{PQT} = 180^\circ - (63^\circ + 66^\circ) = 51^\circ $$

$$ PT = \frac{5}{8} \times 144 = 90\text{ m} $$

$$ QT = \frac{90 \cdot \sin(63^\circ)}{\sin(51^\circ)} \approx 103\text{ m} $$

Question (b)

$$ 27^\circ $$