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The circumference of circle exceeds its diameter by 94 cm.Find the radius of the circle?
Wiki User
∙ 14y ago
Formula for Circumference of a circle is C = pd
C = d+94 therefore
d+94 = pd
1 + 94/d = p
1 + 94/d = 3.142
d = 43.884cm
d = 2r
r = 21.942cm, C = 137.884cm
All figures rounded to 3 decimal places
Wiki User
∙ 14y ago
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In triangle xyz xy equals 6cm yz equals 7cm angle y equals 78 degrees find the length of xz and the measure of angle x give answers to one decimal place?
I know there is a equation to find the answer, but if youae like me someday you will forget it. So, I am going to use trig functions and a little work.Derive the side and angle of a triangleIn triangle xyz, yx equals 6cm, yz equals 7cm, angle y equals 78 degrees find the length of xz and the measure of angle x give answers to one decimal place?I know there is an equation to find the answer, but if you are like me, someday you will forget it. So, I am going to use trig functions and a little work.I wish I wiki would copy MS word drawings, but here we go.Draw a triangle with the base, YX = 6 cm.Label the left end of the line as Point Y.Starting at Point Y, draw a 7 cm line (YZ) up and right from the base YX making an angle of 78º angle with the base.Label the end point of this line as Point Z, so this is line YZThe angle XYZ should open to the right. The only reason I keep repeating this is so your picture looks like mine and you can follow my directions.Connect the points X and Z to complete the triangle.Draw an altitude straight down from point Z.Label the point where the altitude meets the base as point A.The altitude is line ZANow you have 2 right triangles.Look at triangle YZA (left one)Label the 78º angle.Sin θ = opposite ÷ hypotenuseSin 78º = ZA ÷ YZSin 78º = ZA ÷ 7ZA = 6.85 cm (Altitude)Cos θ = adjacent ÷ hypotenuseHypotenuse = YZ = 7 cmAdjacent = line YACos 78º = YA ÷ 7YA = 7 * Cos 78ºYA = 1.46 cmYX = 6 cmYX = YA + AX6 = 1.46 + AXAX = 4.54 cmNow we know the length of 2 sides of the right triangle on the right side, right Triangle ZXA.ZA = 6.85 cm (Altitude)AX = 4.54 cm (adjacent)Tan θ (ZXA) = opposite ÷ adjacentOpposite = ZA (altitude) = 6.85 cmAdjacent= AX = 4.54 cmTan θ (ZXA) = 6.85 ÷ 4.54 cm(ZXA) θ =56.5ºIn the right Triangle ZXA, line ZX is the hypotenuse, the line ZA(Altitude) is the opposite, and the angle between these two lines = 56.5º.Sin θ = opposite ÷ hypotenuseSin 56.5º = Altitude ÷ hypotenuseSin 56.5º = 6.85 ÷ hypotenuseHypotenuse = 6.85 ÷ Sin 56.5ºHypotenuse =8.22 cmZX = 8.22 cmfind the length of xz and the measure of angle x give answers to one decimal place?ZX = 8.22 cm, θ =56.5ºHere is the work from the beginning to the end.ZX = (7 * sin 78º) ÷ (7 * Cos 78º - 6) *-1, tan-1, sin, 1/x, * (7* sin 78º)
