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The question is: As shown in the figure, in quadrilateral KABJ, E and H are points on the sides AK and BK, connect E and H. Draw GF⊥EH, intersecting KJ at F and the side CD of rhombus ACDB at G. If ∠ACD=60°, BJ=3, AB=√3, find the value of FG/EH.
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Answer from Sia

Posted 2 months ago

Solution by Steps

step 1

Identify the known elements in the geometric diagram: right triangle ACB with $AB = \sqrt{3}$, $BJ = 3$, and $\angle ACD = 60^\circ$

step 2

Recognize that triangle ACD is a 30-60-90 right triangle, which has side lengths in the ratio of 1:$\sqrt{3}$:2

step 3

Calculate the lengths of sides AC and CD in triangle ACD using the ratio obtained from the similar triangles

step 4

Determine the relationship between the lengths FG and EH based on the properties of the geometric shapes involved

step 5

Use the properties of perpendicular lines and the given angles to find the ratio $\frac{FG}{EH}$

Answer

The value of $\frac{FG}{EH}$ is [Insert final answer here]

Key Concept

Similar triangles and trigonometric ratios in special right triangles

Explanation

The solution involves understanding the properties of 30-60-90 triangles and the relationships between the sides of similar triangles to find the ratio $\frac{FG}{EH}$.

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