Answer:
see explanation
Step-by-step explanation:
Since Θ is an angle in the third quadrant, then secΘ < 0 and tanΘ > 0
Using the identity
sec x = , then
cos x = -
= - = - = - = - , thus
secΘ = = -
---------------------------
Using the identity
tan x = , then
tanΘ = = - × - =
To solve this problem you must apply the proccedure shown below:
1. You have to r<span>ewrite x=12 in polar form. Then, you have:
12=rCos</span><span>θ
2. Then, you must solve for r, as following:
r=12/Cos</span><span>θ
</span> 3. You have that 1/Cosθ=Sec<span>θ, therefore:
</span> r=12(1/Cos<span>θ)
</span> r=12Sec<span>θ
</span> Therefore, as you can see, the answer is: r=12Secθ<span>
</span>
Answer:
m∠ABG = 20 degrees
m∠BCA = 22 degrees
m∠BAC = 118 degrees
m∠BAG = 59 degrees
DG = 4
BE = 12.4
BG = 11.7
GC = 20.4
Step-by-step explanation:
The given parameters are;
m∠CBG = 20°, m∠BCG = 11°
The incenter of a triangle is the point where the three bisectors of ΔABC meets
m∠ABG = m∠CBG = 20° by definition of angle bisector
m∠ABG = 20°
m∠ACG = m∠BCG = 11° by definition of angle bisector
m∠BCA = m∠ACG + m∠BCG = 11° + 11° = 22°
m∠ABC = m∠ABG + m∠CBG = 20° + 20° = 40°
m∠BAC = 180° - (m∠BCA+m∠ABC) = 180° - (40° + 22°) = 118°
m∠BAG = m∠CAG by definition of angle bisector
m∠BAC = 118° = m∠BAG + m∠CAG = m∠BAG + m∠BAG = 2 × m∠BAG
2 × mBAG = 118°
m∠BAG = 118°/2 = 59°
m∠BAG = 59°
Given that "G" is the incenter of the triangle ABC, we have;
GF = GE = DG = The radius of the incircle of the triangle = 4
Therefore, by Pythagoras' theorem, we have;
BG = √(11² + 4²) = √137 ≈ 11.7
BE = √((BG)² + 4²) = √(137 + 4²) = √153 ≈ 12.4
GC = √(20² + 4²) = √416= 4·√26 ≈ 20.4
9514 1404 393
Answer:
x ≈ 13.7
Step-by-step explanation:
The relevant trig relation is ...
Tan = Opposite/Adjacent
tan(58°) = 22/x
x = 22/tan(58°) ≈ 13.747
The value of x is about 13.7 units.
Possible procedures:
1). peanut, peanut
2). peanut, cashew
3). peanut, pecan
4). cashew, peanut
5). cashew, cashew
6). cashew, pecan
7). pecan, peanut
8). pecan, cashew
9). pecan, pecan.
Nine (9) possible procedures.
But ...
(2) and (4) produce the same final result.
(3) and (7) produce the same final result.
(6) and (8) produce the same final result.
So there are only <em><u>six (6)</u></em> possible different outcomes.