Design a device that will knock a block of wood a distance of 5 meters. this was the challenge in science class. ben and sam designed a pendulum to move the wood block. their first design moved the block about 1.5 meters. they rebuild their pendulum and changed the mass of the pendulum bob. after the changes, the boys knocked the block of wood 4 meters, 6, meters, and finally 8 meters. the average distance the block moved after the final changes to the pendulum was 6 meters. the boys won the design challenge. building the pendulum is which step in the solution process

bd = 9 cm

step-by-step explanation:

in a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. that is, the longest side (hypotenuse) is twice the length of the shortest side.

all of the triangles in your geometry are 30°-60°-90° triangles. ac is the hypotenuse of δacd, and the short side of δabc.

the short side ad of δacd will be half the length of ac, so 3 cm. the hypotenuse ab of δabc will be twice the length of ac, so 12 cm. segment bd is the difference of the lengths ab and ad, so is

bd = ab -ad

bd = 12 cm - 3 cm = 9 cm

comment on side length ratios

you can figure the ratios of side lengths in a 30°-60°-90° triangle by considering the trig ratios of the angles. or you can figure the length of the altitude of an equilateral triangle of side length 2 using the pythagorean theorem.

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explanation:

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