Answer to Question #113355 in Trigonometry for Adams Abayomi

Question

pls i need to know the diagram of this bearing of a village R is 10km from a point P on a bearing 025° from P. Another village A is 6km from P on a bearing 162°. Calculate (a) distance of R from A. (b) bearing of R from A

Answer 1

 Solution

Representing the bearing and distance on a triangle gives:

<RPA = 162 – 25 = 137⁰

[a]      We will use Cosine Rule to determine the distance of R from A (p);

From Cosine Rule;

b² = a² + c² – 2ac Cos B

p² = a² + r² – 2ar Cos P

where

a= 10 km                             Cos P = Cos 137

r = 6km

p = ?

p² = a² + r² – 2ar Cos P

p² = 10² + 6² - 2 (10) (6) Cos 137⁰

p² = 100 + 36 – 120 (- 0.7314)

p² = 136 + 87.76

p² = 223.76

p = 14.95 = 15km (approximated to the nearest km)

[b]      To find the bearing of the R from A,

we will apply Sine Rule;

From Sine Rule;

15 * Sin Ø = 10 * Sin 137 = 6.82

Sin Ø = 6.82/15 = 0.4547

Ø = ArcSin 0.4547 = 27.0^o

Therefore, the bearing of R from A will be

<PRA = 180 – 137 – 27 = 16⁰

The alternating angle to 25^o at R is 65^o

Then, the bearing of R from A = 270 -65-16 = 189⁰