A 15 ft. diagonal brace on a bridge connects a support of the center of the bridge to a side support on the bridge. The horizontal distance that it spans is 3 ft. longer than the height that it reaches on the side of the bridge. Find the horizontal and vertical distances spanned by the brace.

Question

A 15 ft. diagonal brace on a bridge connects a support of the center of the bridge  to a side support on the bridge.  The horizontal  distance that  it spans is 3 ft. longer than the height that it reaches on the side of the bridge.  Find the horizontal and vertical distances spanned by the brace.

campbell_st · Answer

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draw a picture then use pythagoras' theorem for the given information

$$h^2 + (h +3)^2 = 15^2$$

expand and collect like terms

$$2h^2 +6h - -216 = 0$$

solve the quadratic and only use positive values for h.... as distance can only be positive