The answer is A(87).I just plugged the numbers into the Pythagorean Theorem. 200^2 - 180^2 = the square root of 7,600, which equals about 87.
With two dice, you can get sums of between 2 and 12,
tan ( - pie / 12 ) =
- tan ( pie / 12 ) =
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Remainder formula :
tan^2 (x) = [ 1 - 2Cos(2x) ] ÷ [ 1 + 2Cos(2x) ]
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Thus :
tan^2 ( pie/12) =
[ 1 - Cos( 2pie/12 ) ] ÷ [ 1 + Cos( 2pie/12 ) ] =
[ 1 - Cos( pie/6 ) ] ÷ [ 1 + Cos( pie/6 ) ] =
[ 1 - √3/2 ] ÷ [ 1 + √3/2 ] =
[ 2 - √3 / 2 ] ÷ [ 2 + √3 / 2 ] =
[ 2 - √3 ] ÷ [ 2 + √3 ] =
2 - √3 / 2 + √3 =
(2 - √3)(2 - √3) / (2 + √3)(2 - √3) =
(2 - √3)^2 / 4 - 3 =
(2 - √3)^2 / 1 =
(2 - √3)^2
So :
tan^2 ( pie/12 ) = (2 - √3)^2
Take a square root from both sides
tan( pie/12 ) = 2 - √3
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Thus ;
- tan ( pie/12 ) = - ( 2 - √3 )
- tan ( pie/12 ) = - 2 + √3
Approximately :
- tan ( pie/12 ) = - 2 + 1.732
- tan ( pie/12 ) = - 0.268
In this case we know the three sides of the triangle, then this is a SSS triangle (Side Side Side). To solve this case, first we must use the Law of Cosines, applied to the opposite side to the angle we want to find.
We want to find angle W, and its opposite side is XV, then we apply the Law of Cosines to the side XV:
XV^2=XW^2+WV^2-2(XW)(WV)cos W
Replacing the known values:
116^2=96^2+89^2-2(96)(89)cos W
Solving for W
13,456=9,216+7,921-17,088 cos W
13,456=17,137-17,088 cos W
13,456-17,137=17,137-17,088 cos W-17,137
-3,681=-17,088 cos W
(-3,681)/(-17,088)=(-17,088 cos W)/(-17,088)
0.215414326=cos W
cos W = 0.215414326
Solving for W:
W= cos^(-1) 0.215414326
Using the calculator:
W=77.56016397°
Rounded to one decimal place:
W=77.6°
Answer: Third option 77.6°
Answer:
$8.20
Step-by-step explanation:
0.70*4=2.80
1.80*3=5.40
5.40+2.80=8.20
$8.20
