geometry

posted by .

An isosceles triangle has two 10.0-inch sides and a 2w-inch side. Find the radius of the inscribed circle of this triangle, in the cases w = 5.00, w = 6.00, and w = 8.00.
Then Write an expression for the inscribed radius r in terms of the variable w , then find the value of w, to the nearest hundredth, that gives the maximum value of r.

  • geometry -

    The inscribed circle has its centre on the bisectors of the angles.
    Because of the properties of isosceles triangles that angle bisector also becomes the right-bisector of the non-equal side, or our 2w base.

    I will do the w=8 case.

    draw a 10-10-16 triangle, 16 as the base
    label the base angle 2Ø, thus each of the bisected base angles are Ø.
    label the length of the radius on the right-bisector as r, (where the angle bisector meets the righ-bisector of 16)
    cos 2Ø = 8/10 = 4/5
    we know cos 2Ø = 2cos^ Ø - 1
    4/5 = 2cos^2 Ø -
    cos^2Ø = (4/5 + 1)/2 = 9/10
    cosØ = 3/√10
    then sinØ = 1/√10 , using Pythagoras

    back to the triangle, in the smaller right-angled triangle
    tanØ = r/8
    sinØ/cosØ = r/8
    (1/√10)/(3/√10) = r/8
    1/3 = r/8
    r = 8/3

    Now you repeat the calculations for w = 6 and see if you can see the pattern.
    then generalize, or go through the same process, for w.

  • geometry Thanks Reiny -

    Thanks for the help.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. geometry

    An isosceles triangle has two 10.0-inch sides and a 2w-inch side. Find the radius of the inscribed circle of this triangle, in the cases w = 5.00, w = 6.00, and w = 8.00.
  2. geometry

    An isosceles triangle has two 10.0-inch sides and a 2w-inch side. Find the radius of the inscribed circle of this triangle, in the cases w = 5.00, w = 6.00, and w = 8.00. And Write an expression for the inscribed radius r in terms …
  3. geomery

    An isosceles triangle has two 10.0-inch sides and a 2w-inch side. Find the radius of the inscribed circle of this triangle, in the cases w = 5.00, w = 6.00, and w = 8.00. And Write an expression for the inscribed radius r in terms …
  4. geometry

    An isosceles triangle has two 10.0-inch sides and a 2w-inch side. Find the radius of the inscribed circle of this triangle, in the cases w = 5.00, w = 6.00, and w = 8.00.
  5. Geometry

    An isosceles triangle has two 10.0-inch sides and a 2w-inch side. Find the radius of the inscribed circle of this triangle, in the cases w = 5.00, w = 6.00, and w = 8.00. Then Write an expression for the inscribed radius r in terms …
  6. Geometry

    One side of a triangle is x inches longer than another side. The ray bisecting the angle formed by these sides divides the opposite side into 3-inch and 5-inch segments. Find the perimeter of the triangle in terms of x. ( triangle …
  7. GEOMETRY CIRCLES PLEASE

    1.An isosceles triangle with each leg measuring 13 cm is inscribed in a circle . if the altitude to the base is 12 cm find the radius of the circle 2. Circles a and b are tangent at point c. p is on circle a and q is on circle b such …
  8. GEOMETRY CIRCLE

    1.An isosceles triangle with each leg measuring 13 cm is inscribed in a circle . if the altitude to the base is 12 cm find the radius of the circle 2. Circles a and b are tangent at point c. p is on circle a and q is on circle b such …
  9. GEOMETRY CIRCLES PLEASE

    HELP ME PLEASE. 1.An isosceles triangle with each leg measuring 13 cm is inscribed in a circle . if the altitude to the base is 12 cm find the radius of the circle 2. Circles a and b are tangent at point c. p is on circle a and q is …
  10. geometry (check answers)

    Determine whether you can construct many, one, or no triangle(s) with the given description. a) a triangle with angle measures of 50°, 70°, and 100° no b) a triangle with one angle measure of 60° and one 4-centimeter side no c) …

More Similar Questions