The hypotenuse of a right-angled triangle is 12 cm. Base angle is 30 degrees. Find the other sides.
We know, sin(x)=height/hypotenuse. Therefore, sin(30)=1/2=height/12 height=6cm. Also, cos(x)= base/hypotenuse cos(30)=(3^(0.5))/2=1.732/2=0.866=base/12 base=10.392 cm.
The radius of a circle is 5cms. Find the area of the circle.
We know, the area of a circle is given by (pi)(r^2) pi=3.14 and r=5. Therefore, area= 3.14*5*5 area=78.50cm^2.
The area of a rectangle is 84 cm squared. The breadth is 5 cm shorter than the length. What are the side lengths of the rectangle?
Let the length of the rectangle be x. Therefore, breadth is (x-5). x.(x-5)=84 x^2-5x-84=0 x^2-12x+7x-84=0 x.(x-12)+7(x-12)=0 (x+7)(x-12)=0 x is the length and hence cannot be a -ve value. Hence, x=12. length=12cm. breadth=7cm.