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.
Explanation
(a) They sketched the required diagram as follows:
(b) (i), using sine rule (frac{285}{sin z} = frac{307}{sin 307})
Then sin z (frac{285 times sin 78^o}{307} = frac{285 times 0.9781}{307}) = 0.9080
Z = (sin^{-1}(0.9080)) = 65.23(^o)
The bearing of X from Z = 360(^o) – 65.23(^o) = 294.77(^o) (approx) 295(^o) or N65(^o)W correct to the nearest whole number.
(b)(ii) They obtained < YXZ = 180(^o) – 143.23(^o) = 36.77(^o)
Then, using sine rule, (frac{text{|YZ|}}{sin 36.77^o} = frac{307}{sin 78^o}) and computing for |YZ|,
|YZ| = (frac{307 times 0.5986}{0.9781}) = 187.88m
and Therefore, the distance between Y and Z (approx) 188 m correct to the nearest whole number