A wooden stake, S, is 13m from a point, A, on a straight fence. SA makes an angle of 20 degrees with the fence. If the goat is tethered to S by a 10m rope, where, on the fence, is the nearest point to A at which it can graze?
2007-06-15 06:48:25 · 4 answers · asked by gab BB 6 in Science & Mathematics ➔ Mathematics
If the required point is S, then in triangle SPA:
SA = 13m
SP = 10m
Angle SAP = 20deg
Using the sine rule:
sin(SPA) = 13sin(20)/10 and it is clear from the diagram that SPA is obtuse.
The exterior angle of the triangle at P is therefore 26.40deg.
Angle PSA is therefore 26.40 - 20 = 6.40deg.
Using the cosine rule:
PA^2 = 13^2 + 10^2 - 2*13*10cos(6.40deg)
= 169 + 100 - 260cos(6.40)
PA = sqrt(269 - 260cos(6.40))
= 3.26m.
The goat can get no closer than 3.26m from A.
2007-06-15 07:18:05 · answer #1 · answered by Anonymous · 0⤊ 0⤋
S,A and the nearest point on fence from S forms a right triangle. So using the basic definition of trigonometric functions,
Cos 20 = The dimension in question / 13; so the answer is 13 Cos 20.
2007-06-15 13:58:09 · answer #2 · answered by arun 3 · 0⤊ 1⤋
13-10 = 3 m
2007-06-15 14:02:27 · answer #3 · answered by ironduke8159 7 · 0⤊ 0⤋
3m from A.
2007-06-15 13:54:27 · answer #4 · answered by fcas80 7 · 0⤊ 0⤋