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In rectangle ABCD, ∡BAC=30° and AD=50. What is the length of side DC?25.028.943.386.6

User Arturwwl
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1 Answer

26 votes
26 votes

With the informationabout the rectangle, we can say the angle between the diagonal and the longest side (unknown) is 30°. While the shortest side is 50.

Then, to estimate the length of the remaining side (DC, which is equal to AB), we can state the following relationship:


\tan 30^o=(50)/(AB)=(50)/(DC)

Then:


DC=(50)/(\tan30^o)=\frac{50}{\sqrt[]{3}/3}=\frac{3\cdot50}{\sqrt[]{3}}

We can multiply numerator and denominator by square root of 3 to simplify:


DC=\frac{3\cdot50}{\sqrt[]{3}}=\frac{\sqrt[]{3}\cdot3\cdot50}{\sqrt[]{3}\cdot\sqrt[]{3}}=\frac{\sqrt[]{3}\cdot3\cdot50}{3}=50\sqrt[]{3}\approx86.6

The length of side DC is approximately 86.6. The correct answer is the fourth option.

In rectangle ABCD, ∡BAC=30° and AD=50. What is the length of side DC?25.028.943.386.6-example-1
User Taylor Lopez
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