Andi berangkat sekolah jam 06.45 WIB, sampai sekolah jam 07.05 WIB. berapa waktu yang dibutuhkan Andi sampai ke sekolah dalam satuan menit?
Answer (4)
Ok so we need to subtract the area of the triangle from the area of the segment and this will equal 100. We know that the area of the segment is: 360 80 ∗ π r 2 And that the area of the triangle is: 2 1 r 2 s in ( 80 ) Therefore: 360 80 ∗ π r 2 − 2 1 r 2 s in ( 80 ) = 100 We can simplify it through these steps: 360 80 ∗ π r 2 − 2 1 r 2 s in ( 80 ) = 100 4 π r 2 − 9 r 2 s in ( 80 ) = 1800 r 2 ( 4 π − 9 s in ( 80 )) = 1800 r 2 = 4 π − 9 s in ( 80 ) 1800 r = 4 π − 9 s in ( 80 ) 1800 Therefore r=22.04cm (4sf)
Hello,
The formula for finding the area of a circular region is: A = 2 α ∗ r 2
then: A 1 = 2 80 ∗ r 2
With the two radius it is formed an isosceles triangle, so, we must obtain its area, but first we obtain the height and the base.
cos ( 40 ) = r h h = r ∗ cos ( 40 ) se n ( 40 ) = r b b = r ∗ se n ( 40 )
Now we can find its area: A 2 = 2 ∗ 2 b ∗ h A 2 = [ r ∗ se n ( 40 )] [ r ∗ cos ( 40 )] A 2 = r 2 ∗ se n ( 40 ) ∗ cos ( 40 )
The subtraction of the two areas is 100cm^2, then:
A 1 − A 2 = 100 c m 2 ( 40 ∗ r 2 ) − ( r 2 ∗ se n ( 40 ) ∗ cos ( 40 )) = 100 c m 2 39.51 r 2 = 100 c m 2 r 2 = 2.53 c m 2 r = 1.59 c m
Answer: r= 1.59cm
To find the radius r when the area of the shaded segment is 100 cm², we used the formulas for the area of the segment and the triangle formed by the radius lines. By setting up the equation and solving for r , we found that r ≈ 22.04 cm . This radius is derived from the geometry of the situation and trigonometric properties.
;
Jawaban:06.45 - 07.05 = 20 menitAndi sampai ke sekolah dlm 20 menit
