Answer:
1.3 pounds
Step-by-step explanation:
Answer:
s = 130 degrees
Step-by-step explanation:
decagon has a 1,440 degrees interior angles
equation: 1,440 = s + 1310
to find s, add all the known angles
⇒ s + 150 + 170 + 160 + 130 +120 + 160 + 105 + 160 +155
⇒ s + 1,310
equation:
s + 1310 = 1440
subtract each side by 1310
⇒ s + 1310 - 1310 = 1440 - 1310
⇒ s = 130
Answer:
12.1 cm
Step-by-step explanation:
Using the law of sines, we can find angle C. Then from the sum of angles, we can find angle B. The law of sines again will tell us the length AC.
sin(C)/c = sin(A)/a
C = arcsin((c/a)sin(A)) = arcsin(8.2/13.5·sin(81°)) ≈ 36.86°
Then angle B is ...
B = 180° -A -C = 180° -81° -36.86° = 62.14°
and side b is ...
b/sin(B) = a/sin(A)
b = a·sin(B)/sin(A) = 13.5·sin(62.14°)/sin(81°) ≈ 12.0835
The length of AC is about 12.1 cm.
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<em>Comment on the solution</em>
The problem can also be solved using the law of cosines. The equation is ...
13.5² = 8.2² +b² -2·8.2·b·cos(81°)
This is a quadratic in b. Its solution can be found using the quadratic formula or by completing the square.
b = 8.2·cos(81°) +√(13.5² -8.2² +(8.2·cos(81°))²)
b = 8.2·cos(81°) +√(13.5² -(8.2·sin(81°))²) . . . . . simplified a bit
Answer:
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