Question

ABCD is a rectangle and AD is 8 cm and CD is 12 cm. A line segment CE is drawn , making an angle of 60 degree with AB intersecting AB in E. Find the length of CE and BE

Answer 1

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Answer 2

Answer:

The length of BE = 4.62 cm and CE = 9.24 cm.

Step-by-step explanation:

• In a rectangle opposite sides are equal. So in ABCD triangle,

               BC = AD = 8 cm.  and AB = CD = 12 cm

• Now from the diagram we can see ΔBCE is a right angle triangle and ∠BEC = 60°.
• As we know tanФ = $\frac{height}{base}$ ,

        so in ΔBCE tan60° = $\frac{BC}{BE}$  [BC = height = 8cm and BE = base]

                           tan60° = $\frac{8}{BE}$

                           BE = 8/tan60° = 8/√3 = 4.62 cm

        ∴ The length of BE= 4.62 cm

• By applying Pythagoras theorem in  ΔBCE we get,

               CE² = BE² + BC²

              CE² = 4.62² + 8²

              CE² = 21.34 + 64 = 85.34

              CE = √85.34 = 9.24 cm

     ∴ The length of CE = 9.24 cm.

                           

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