Kuulchat - Senior High School (S.H.S) Mathematics Bearing & Distance Practice Test Questions

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BEARING & DISTANCE

1.

A man travels 4 km from a point I on a bearing of 135° to J. He continues 13 km on a bearing of 045° to K.

(a)

Illustrate the information in a diagram.

(b)

Find:

(i)

correct to two significant figures, |JK|;

(ii)

the bearing of K from I.

Show Solution

(a)

Note: Bearing starts from the North clockwise.

(b)

(i)

Pythagorean Theorem

The hypothenuse (c) is the longest side. The side facing the right-angle (∟)

|JK|² = 4² + 13²

|JK|² = 185

Take square root of both sides.

|JK|² = $\sqrt{185}$ = 13.6 km ≈ 14 km (two significant figures)

(ii)

tan θ = $\frac{13 km}{4 km}$

θ = tan^-1( $\frac{13}{4}$ ) = 72.9° ≈ 73°

Bearing of K from I + θ = 135°

Bearing of K from I = 135° - θ

Bearing of K from I = 135° - 73°

Bearing of K from I = 62°

Bearing of K from I is 062°

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BEARING & DISTANCE

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