Answer:
good luck
Step-by-step explanation:
Answer:
541.67m²
Step-by-step explanation:
Step 1
We find the third angle
Sum of angles in a triangle = 180°
Third angle = Angle V = 180° - (63 + 50)°
= 180° - 113°
Angle V = 67°
Step 2
Find the sides x and v
We find these sides using the sine rule
Sine rule or Rule of Sines =
a/ sin A = b/ Sin B
Hence for triangle VWX
v/ sin V = w/ sin W = x / sin X
We have the following values
Angle X = 50°
Angle W = 63°
Angle V = 67°
We are given side w = 37m
Finding side v
v/ sin V = w/ sin W
v/ sin 67 = 37/sin 63
Cross Multiply
sin 67 × 37 = v × sin 63
v = sin 67 × 37/sin 63
v = 38.22495m
Finding side x
x / sin X= w/ sin W
x/ sin 50 = 37/sin 63
Cross Multiply
sin 50 × 37 = v × sin 63
x = sin 50 × 37/sin 63
x = 31.81082m
To find the area of triangle VWX
We use heron formula
= √s(s - v) (s - w) (s - x)
Where S = v + w + x/ 2
s = (38.22 + 37 + 31.81)/2
s = 53.515
Area of the triangle = √53.515× (53.515 - 38.22) × (53.515 - 37 ) × (53.515 - 31.81)
Area of the triangle = √293402.209
Area of the triangle = 541.66614164081m²
Approximately to the nearest tenth = 541.67m²
Answer:
1 m/s2
Step-by-step explanation:
Olive Oyl's weight = 10 × 9.81 = 98.1 N
This weight is a force acting downward because it is due to gravity.
Popeye pulls Olive Oyl up with a force of 108.1 N. Both forces act vertically but in opposite directions. Hence their resultant, R, is their difference and is in the direction of the larger force.
R = 108.1 N - 98.1 N = 10 N
This force causes an acceleration, a, on the mass, m, of Popeye.
R = ma
a = R/m = 10 N/10 kg = 1 m/s2
For this case we use the following formula
Area of Sector = Area * radians of sector / 2 * pi radians
Where,
Area: it is the area of the complete circle.
We have then:
Area = pi * r ^ 2
Area = pi * (6) ^ 2
Area = 36pi
Substituting values:
5pi = 36pi * radians of sector / 2 * pi
Clearing:
radians of sector = ((5pi) * (2pi)) / (36pi)
radians of sector = (10pi ^ 2) / (36pi)
radians of sector = (10pi) / (36)
radians of sector = (10/36) pi
radians of sector = (5/18) pi
in degrees:
(5/18) pi * (180 / pi) = 50 degrees
Answer:
The measure of the central angle is:
50 degrees
Answer:
You can use either of the following to find "a":
- Pythagorean theorem
- Law of Cosines
Step-by-step explanation:
It looks like you have an isosceles trapezoid with one base 12.6 ft and a height of 15 ft.
I find it reasonably convenient to find the length of x using the sine of the 70° angle:
x = (15 ft)/sin(70°)
x ≈ 15.96 ft
That is not what you asked, but this value is sufficiently different from what is marked on your diagram, that I thought it might be helpful.
__
Consider the diagram below. The relation between DE and AE can be written as ...
DE/AE = tan(70°)
AE = DE/tan(70°) = DE·tan(20°)
AE = 15·tan(20°) ≈ 5.459554
Then the length EC is ...
EC = AC - AE
EC = 6.3 - DE·tan(20°) ≈ 0.840446
Now, we can find DC using the Pythagorean theorem:
DC² = DE² + EC²
DC = √(15² +0.840446²) ≈ 15.023527
a ≈ 15.02 ft
_____
You can also make use of the Law of Cosines and the lengths x=AD and AC to find "a". (Do not round intermediate values from calculations.)
DC² = AD² + AC² - 2·AD·AC·cos(A)
a² = x² +6.3² -2·6.3x·cos(70°) ≈ 225.70635
a = √225.70635 ≈ 15.0235 . . . feet
