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Given that m∠JKL = 94°, m∠KLJ = 41°, and the radius of the circle is 10 units, find s, rounded to the nearest hundredth.

Respuesta :

calculista
the picture in the attached figure

step 1
find the m ∠ KJL

we know that
m ∠ KJL+m ∠ JKL+m ∠ KLJ=180° -----> by the sum of the internal angles of a triangle is 180 degrees
so
m ∠ KJL=180°-(m ∠ JKL+m ∠ KLJ)
m ∠ KJL=180°-(94°+41°)
m ∠ KJL=45°

if m ∠ KJL=45°
then
 m arc s=45°------> by central angle

step 2
by proportion
central angle/360°=arc length s/(2*pi*r)
arc length s=(45°/360°)*(2*pi*10)
arc length s=7.85 units

the answer is
the arc length s is 7.85 units

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