Answer/Step-by-step explanation:
Recall the acronym SOHCAHTOA. This is what we would apply as appropriate in each case.
8. θ = 40°
Opp = m
Adj = 20
Thus, apply TOA
Tan (θ) = opp/adj
Plug in the values
Tan (40) = m/20 (equation)
20×Tan(40) = m
m = 16.7820
9. θ = 22°
Hyp = w
Adj = 18
Thus, apply CAH
Cos (θ) = adj/hyp
Plug in the values
Cos 22 = 18/w (equation)
w×cos 22 = 18
w = 18/(cos 22)
w = 19.4136
10. θ = 35°
Hyp = 55
Opp = x
Thus, apply SOH
Sin θ = opp/hyp
Plug in the values
Sin 35 = x/55 (equation)
55×sin 35 = x
x = 31.5467
11. θ = 33°
Hyp = 19
Adj = x
Thus, apply CAH
Cos θ = adj/hyp
Plug in the values
Cos 33 = x/19 (equation)
19×cos 33 = x
x = 15.9347
12. θ = 17°
Opp = 7
Hyp = x
Thus, apply SOH
Sin θ = opp/hyp
Plug in the values
Sin 17 = 7/x (equation)
x×sin 17 = 7
x = 7/(sin 17)
x = 23.9421
13. θ = 40°
Opp = 15
Adj = x
Thus, apply TOA
Tan θ = opp/adj
Plug in the values
Tan 40 = 15/x (equation)
x×Tan 40 = 15
x = 15/(Tan 40)
x = 17.8763
Answer:
The coordinates of the point P is -3
Please see attached number line
Step-by-step explanation:
The given information are;
The length of the given number line = The line extends from -30 to +10
The location of major tick marks = Every ten numbers
The location of minor tick marks = Every number
The location of the point P = Three ticks to the left of 0
Therefore, the coordinates of the point P = -3
Answer:
m<1 = 69°
Step-by-step explanation:
Angles 20x + 11 and 25x - 14 are vertical angles, so they are congruent.
25x - 14 = 20x + 11
5x = 25
x = 5
The actual measure of angle 20x + 11 is 20(5) + 11 = 111°.
Angle 20x + 11 and <1 are supplementary, so the sum of their measures is 180°.
m<1 + 111° = 180°
m<1 = 180° - 111°
m<1 = 69°
Answer:
20% decrease
Step-by-step explanation:
Start by dividing 40 by 50.
40/50 = 0.8
0.8 is the decimal form of 80%. So now we know that 40 is 80% of 50. This means that the remaining 20% is the difference between the books read in November and December.
Answer:
11th floor
Step-by-step explanation:
So to figure out what floor Rosa's office is in, we need to declare some variables.
x = Rosa's office
down 5 floors = -5
up 8 floors = 8
down 13 floors = - 13
One major clue to find Rosa's office is that she went down 13 floors to get to the 1st floor. So let's declare that Rosa is on the first floor.
x - 5 + 8 - 13 = 1
x - 10 = 1
x = 1 + 10
x = 11
So Rosa's office is at the 11th floor of the building.