Answer:
Step-by-step explanation:
So you can use the special formula for 30-60-90 triangle or you can use the whole Soh Cah Toa thing.
I honestly prefer trig. so a is the opposite side of the 30 deg and 12 is the hyp. This should scream sine to you since sine goes with opposite/hypotenuse.
sin(30 deg)=a/12
Multiply both sides by 12
giving a=12 sin(30)
Type into calculator unless you know your unit circle well.
a=6
Answer:
Ted is 6 years old
Leon is 7 years old
Andrew is 8 years old
Step-by-step explanation:
Ted+Leon=13 ⇒T+L=13 ⇒L=13-T
Leon+Andrew=15 ⇒L+A=15 ⇒A=15-L ⇒A=15-(13-T) because Leon =13-Ted
A=2+T
Ted+Andrew=14
T+A=14 ( substitute Andrew age from A=2+T)
T+2+T=14
2T=12
<h2>T=12/2=6 (Ted is 6 years old)</h2><h2>A=2+T=2+6=8 ( Andrew is 8 years old)</h2><h2>Leon=13-T=13-6=7 ( Leons is seven years old)</h2>
check: Ted+Leon=13 ⇒ 6+7=13
Leon + Andrew=15 ⇒7+8=15
Andrew+Ted=14 ⇒ 6+8=14
It's difficult to make out what the force and displacement vectors are supposed to be, so I'll generalize.
Let <em>θ</em> be the angle between the force vector <em>F</em> and the displacement vector <em>r</em>. The work <em>W</em> done by <em>F</em> in the direction of <em>r</em> is
<em>W</em> = <em>F</em> • <em>r</em> cos(<em>θ</em>)
The cosine of the angle between the vectors can be obtained from the dot product identity,
<em>a</em> • <em>b</em> = ||<em>a</em>|| ||<em>b</em>|| cos(<em>θ</em>) ==> cos(<em>θ</em>) = (<em>a</em> • <em>b</em>) / (||<em>a</em>|| ||<em>b</em>||)
so that
<em>W</em> = (<em>F</em> • <em>r</em>)² / (||<em>F</em>|| ||<em>r</em>||)
For instance, if <em>F</em> = 3<em>i</em> + <em>j</em> + <em>k</em> and <em>r</em> = 7<em>i</em> - 7<em>j</em> - <em>k</em> (which is my closest guess to the given vectors' components), then the work done by <em>F</em> along <em>r</em> is
<em>W</em> = ((3<em>i</em> + <em>j</em> + <em>k</em>) • (7<em>i</em> - 7<em>j</em> - <em>k</em>))² / (√(3² + 1² + 1²) √(7² + (-7)² + (-1)²))
==> <em>W</em> ≈ 5.12 J
(assuming <em>F</em> and <em>r</em> are measured in Newtons (N) and meters (m), respectively).
Answer:
b
Step-by-step explanation:
A^2 + B^2 = C^2 - Right Triangle Formula
8^2 + 7^2 = 6^2 - Plug it into the formula
64 + 49 = 36 - Solve
64 = 85 - Add B and C
21 - your answer
Hopefully this helps.
