Richard mows 1/3 of his yard in 1/2 hour. how much of his yard would Richard mow in 1 hour
1 answer:
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Answer:
see explanation
Step-by-step explanation:
Using the double angle identity for sine
sin2x = 2sinxcosx
Consider left side
cos20°cos40°cos80°
= (2sin20°cos20°)cos40°cos80°
= (2sin40°cos40°)cos80°
= (sin80°cos80° )
= (2sin80°cos80° )
= . sin160°
= . sin(180 - 20)°
= . sin20°
= = right side , thus proven
Answer:
∠RST = 120°
Step-by-step explanation:
We assume the positions of the lines and angles will match the attached figure. The angle addition theorem gives a relation that can be solved for x, then for the value of angle RST.
∠RSU +∠UST = ∠RST
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78° + (3x -12)° = (6x +12)° . . . . . substitute given values into the above
54 = 3x . . . . . . . . . . . . . . . . divide by °, subtract 3x+12
108 = 6x . . . . . . . . . . . multiply by 2
120° = (6x +12)° = ∠RST . . . . add 12, show units
The measure of angle RST is 120 degrees.
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<em>Additional comment</em>
Note that we don't actually need to know the value of x (18) in this problem. We only need to know the value of 6x.
