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faltersainse [42]
3 years ago
9

A plot of land has been surveyed for a new housing development with borders AB, BC, DC, and DA. The plot of land is a right trap

ezoid with a height of 60 feet and an opposite leg length of 65 feet.
Mathematics
1 answer:
Doss [256]3 years ago
6 0

Answer:

m∠ABC = 119° and DC = 105 feet

Step-by-step explanation:

For better understanding of the solution see the attached figure of the trapezium ABCD :

m∠BCD = 61°

By using the property, Sum of interior opposite angles in a trapezium is supplementary ⇒ m∠BCD + m∠ABC = 180°

⇒ m∠ABC = 180° - 61°

⇒ m∠ABC = 119°

Now, to find length of DC,

Draw a perpendicular BE on CD ⇒ CD = DE + EC

AB = DE

⇒ DE = 80 feet

In ΔBEC, By using Pythagoras theorem

EC² = BC² - BE²

⇒ EC² = 65² - 60²

⇒ EC = 25 feet

Hence, DC = 80 + 25

= 105 feet

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