Question

The length of the diagonal of a Rectangle is 14cm,and it forms a 30 degree angle in one corner of the rectangle.What is the area of the rectangle.(A=LxW)

Answer 1

We can find W and L using the sine and the cosine functions:

`\begin{gathered} \sin (30)=(W)/(14) \\ so\colon \\ W=14\cdot\sin (30) \\ --------- \\ \cos (30)=(L)/(14) \\ so\colon \\ L=14\cdot\cos (30) \end{gathered}`

Therefore:

`\begin{gathered} A=L\cdot W \\ A=14\cdot\cos (30)\cdot14\cdot\sin (30) \\ A=49\sqrt[]{3} \\ A\approx84.87cm^2 \end{gathered}`

Answer:

84.87 cm²