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IB Mathematics: Applications and Interpretation SL · 12.10: Geometry & Trigonometry · 12.10.12
Name Date
Grazing goat problems: sector and triangle area Problem set B
Split the grazed region into triangles and sectors. Check that the calculator's angle mode matches the angles you use. Give answers to 3 significant figures unless a question says otherwise.
Each question matches the question with the same number in set A. Do the ones you got wrong there.
Difficulty: first skills applying them stretch
Skills
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A field is a right-angled triangle with sides 7 m, 24 m and 25 m. A cow, a horse and a donkey are each tied to a different corner by a 3 m rope. The ropes are too short to meet, and the animals cannot leave the field.
- (a) Find the area each animal can graze.
- (b) Which animal grazes the most?
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A field is a right-angled triangle with sides 12 m, 16 m and 20 m. Three llamas are each tied to a different corner by a 5 m rope. The ropes are too short to meet, and the llamas cannot leave the field. Find the percentage of the field the llamas graze altogether.
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A field is a rectangle 11 m by 4 m. A pony is tied by a 5.5 m rope to a post at one corner. Find the area of the field the pony can graze.
In context
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A garden is a right-angled triangle with sides 15 m, 20 m and 25 m. A llama is tied to the midpoint of the hypotenuse by a rope just long enough to reach both ends of it. A second llama is tied to the midpoint of the 20 m side by a 10 m rope. Neither llama can leave the garden.
- (a) Find the percentage of the garden the first llama can graze.
- (b) The hypotenuse cuts a segment off the circle of the second llama. Find the area the second llama can graze.
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A rectangular school field measures 14 m by 5 m. A tethered ram is tied by a 7 m rope to a post at one corner of the field. Find the percentage of the field the ram can graze, to the nearest integer.
jmaths.xyz · AI SL · 12.10.12 Grazing goat problems: sector and triangle area