Given a rectangle with a diagonal of 3 cm, an angle of 37 degrees between the diagonal and the base.
| April 28, 2021 | education
Given a rectangle with a diagonal of 3 cm, an angle of 37 degrees between the diagonal and the base. find the area of the rectangle.
In a right-angled triangle ACD:
Cos37 = AD / AC.
AD = AC * Cos370 = 3 * Cos37.
Sin37 = CD / AC.
SD = AC * Cos370.
Then the area of the rectangle ABCD is equal to:
Savsd = AD * CD = 3 * Cos37 * 3 * Sin37 = 9 * (Sin (37 – 37) + Sin (37 + 37)) / 2 = 4.5 * Sin740 cm2.
Answer: The area of the rectangle is 4.5 * Sin740 cm2.
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