Take a bow

Geometry Level 5

You're lost amidst the jungle. Your bow was broken when you've fell a ravine. The only thing you carry with you is a pocket knife, a tape-measure and some arrows in a bag. It's darkening and you can feel a chill in your spine, since fierce animals had started to roam by their habitat.

You climb a tree, find some strong bindweed and cogitate if can make a bow to your arrows.

Suppose you had found bindweed enough to weave a rope of $$50 cm$$. You're a skilled archer and know that for maximum precision of an arrow shot the arrow must have $$\frac {2} {3}$$ of the bow length and that distance between the middle point of the bow and the middle point of the rope must be $$\frac {1} {3}$$ of the arrow length. Your arrows have $$25 cm$$.

What must be the opening (in degrees) of the bow? Give your answer to 2 decimal places.

Details and assumptions

• A bow is intended to be a circular section, which points have all the same distances from a single point, the centre of a circumference. Radius is the distance between this single point and any point of the bow;

• If you need some trigonometrical functions, $$\sin (53.13º)=0.8$$

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