A man starts from a point X and walk 285 m to Y on a bearing of 078\(^o\). He then walks due South to a point Z which is 307 m from X. (a) Illustrate the in...
Question 1 Report
A man starts from a point X and walk 285 m to Y on a bearing of 078\(^o\). He then walks due South to a point Z which is 307 m from X.
(a) Illustrate the information on a diagram.
(b) Find, correct to the nearest whole number, the:
(i) bearing of X from Z;
(ii) distance between Y and Z.
Answer Details
(a) Diagram: from X, line XY runs at bearing \(078^{\circ}\) (285 m); from Y the man walks due south to Z; XZ \(= 307\) m closes the triangle.
Place X at the origin:
\[Y = (285\sin 78^{\circ},\ 285\cos 78^{\circ}) = (278.8,\ 59.3)\]Z has the same easting as Y (a due-south move): \(Z = (278.8,\ z)\).
\[|XZ| = 307:\ 278.8^2 + z^2 = 307^2 \Rightarrow z^2 = 16520 \Rightarrow z = -128.5\](b)(ii) Distance YZ \(= 59.3 - (-128.5) = 187.8 \approx 188\) m.
(b)(i) Bearing of X from Z. \(\vec{ZX} = (-278.8,\ 128.5)\), pointing north-west.
\[\text{angle west of north} = \tan^{-1}\frac{278.8}{128.5} = 65^{\circ} \Rightarrow \text{bearing} = 360^{\circ} - 65^{\circ} = 295^{\circ}\]Download The App On Google Playstore
Everything you need to excel in your exams
