Given: abcd - rectangle

area of abcd = 458m2

m∠aob = 80°

find: ab, bc

AB = 19.60 m and BC = 23.37 m to the nearest hundredth.

Step-by-step explanation:

The sides OA OB OC and OD are all equal and we have 2 pairs of equal isosceles triangles formed.

One with angles 80 & 2*50 and another pair with angles 100 and 2*40 degrees.

Consider the triangle with AB as the base.

Applying the Sine Rule we have:

AB / sin 80  = OA  / sin 50  so  AB = OA sin 80 / sin 50

Consider now the triangle BOC:

BC / sin 100 = OB / sin 50 = OA / sin 50 ( because OA = OB).

So BC = OA sin 100 / sin 40

Therefore AB /BC =   (OA sin 80 / sin 50)  /  (OA sin 100 / sin 40)

=  sin 80 * sin 40 / sin 50 sin 100

= 0.8391

and BC = AB / 0.8391.

Now we are given that the area = AB * BC = 458.

Therefore substituting for BC we have:

AB * AB / 0.8391 = 458

AB^2 = 458 * 0.8391

=  384.31

AB = 19.60

and BC = 458/19.60

= 23.37.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

answer: 1722

step-by-step explanation:

given: the mass of saturn=

the mass of mercury=

the number of times the mass of saturn is greater than the mass of mercury

hence, the mass of saturn is 1722 times greater than the mass of mercury.