The diagonal AC of the rectangle ABCD is 6 cm and makes an angle of 46 degrees with the side AD. Find the area ABCD.
| September 17, 2021 | education
The AC diagonal divides a right-angled triangle into two equal-sized right-angled triangles.
In a right-angled triangle ACD Cos46 = AD / AC.
AD = AC * Cos46 = 6 * Cos46.
Sin46 = CD / AC.
CD = AC * Cos460 = 6 * Cos46.
Then the area of the rectangle ABCD is equal to:
Savsd = AD * CD = 6 * Cos46 * 6 * Sin46 = 36 * (Sin (46 – 46) + Sin (46 + 46)) / 2 = 18 * Sin92 cm2.
Answer: The area of the rectangle is 18 * Sin920 cm2.
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