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Damm [24]
3 years ago
7

A semicircle is inscribed in an isosceles triangle with base 16 and height 15 so that the

Mathematics
1 answer:
ira [324]3 years ago
8 0

Answer:

  7 1/17

Step-by-step explanation:

A figure can be helpful.

The inscribed semicircle has its center at the midpoint of th base. It is tangent to the side of the isosceles triangle, so a radius makes a 90° angle there.

The long side of the isosceles triangle can be found from the Pythagorean theorem to be ...

  BC² = BD² +CD²

  BC² = 8² +15² = 289

  BC = √289 = 17

The radius mentioned (DE) creates right triangles that are similar to ∆BCD. In particular, we have ...

  (long side)/(hypotenuse) = DE/BD = CD/BC

  DE = BD·CD/BC = 8·15/17

  DE = 7 1/17 ≈ 7.059

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