The radius of a circle is 2 inches. What is the area of a sector bounded by a 90° arc?
1 answer:
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Answer:
Option 2: m∠1 = 147°, m∠2 = 80°, m∠3 = 148°
Step-by-step explanation:
Step 1: Consider triangle ABC from the picture attached below.
Lets find angle x
x + 47 + 33 = 180 (because all angles of a triangle are equal to 180°)
x = 100°
Angle x = Angle y = 100° (because vertically opposite angles are equal)
Step 2: Find angle 2
Angle 2 = 180 - angle x (because angle on a straight line is 180°)
Angle 2 = 180 - 100
Angle 2 = 80°
Step 3: Find angle z
48 + y + z = 180° (because all angles of a triangle are equal to 180°)
z = 32°
Angle 3 = 180 - angle z (because angle on a straight line is 180°)
Angle 3 = 180 - 32
Angle 3 = 148°
Step 4: Find angle 1
Angle 1 = 180 - 33 (because angle on a straight line is 180°)
Angle 1 = 147°
Therefore m∠1 = 147°, m∠2 = 80°, m∠3 = 148°
Option 2 is correct
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Answer:
<em>A ≈ 28.5</em>
Step-by-step explanation:
a, b, c
P = a + b + c
Semiperimeter s =
A =
~~~~~~~~~~~~~~~
= 4.3 + 2.89 + 6.81 = 14
s = 14 ÷ 2 = 7
=
= √14.75901 ≈ 3.84
= 8.59 + 7.58 + 6.81 = 22.98
s = 22.98 ÷ 2 = 11.49
=
= √609.7343148 ≈ 24.6928
= 3.84 + 24.6928 ≈ <em>28.5</em>