(a) A cottage is on a bearing of 200° and 110° from Dogbe’s and Manu’s farms respectively. If Dogbe walked 5 km and Manu 3 km from the cottage to their farms, find, correct to: (i) two significant figures, the distance between the two farms, (ii) the nearest degree, the bearing of Manu’s farm from Dogbe’s.
(b) A ladder 10 m long leaned against a vertical wall xm high. The distance between the wall and the foot of the ladder is 2 m longer than the height of the wall.
Calculate the value of x
Explanation
diagram above(i)
(i) Distance between Manu and Dogbe's farm =√(3\(^2\)+5\(^2\))
= 5.83km or 5.8 km
(i) tanØ = 0.6
Ø= tan\(^{-1}\) (O.6)
= 30.96°
Bearing = 30.96°+200° =230.96
= 231° (nearest degree)
(b) x\(^2\) + (x+2)\(^2\) = 10\(^2\)
2x\(^2\) + 4x - 96 = 0
(x-6) (x+8) = 0
x = 6,x = -8
: x = 6cm