Answer:
length of the zip line = 121. 63 ft
Step-by-step explanation:
The length of the zip line AB forms a triangle ABC. To find the length AB we need to know the length of 2 sides of the triangle an angle.
Triangle ADC
We need to find the hypotenuse side AC using the SOHCAHTOA principle.
Therefore,
sin 41° = opposite/hypotenuse
opposite = 65 ft
sin 41° = 65/AC
cross multiply
0.65605902899
AC = 65
divide both sides by 0.65605902899
AC = 65/0.65605902899
AC = 99.0764506359 ft
AC ≈ 99.08 ft
Triangle BCE
We are looking for side BC. The triangle BCE is also a right angle triangle so we use the same methodology like the triangle ADC.
sin 62° = opposite/hypotenuse
opposite = 85 ft
sin 62° = 85/BC
cross multiply
BC sin 62° = 85
BC = 85/sin 62°
BC = 85/0.88294759285
BC = 96.2684543086
BC ≈ 96.27 ft
The angle ACB can be gotten when you subtract 62° and 41° from 180 (angle on a straight line).
Therefore,
∠ACB = 180° - 62° - 41°
∠ACB = 77°
Now let us use the cosine law to find the zip line AB.
c² = a² + b² - 2ab cos C
a = 96.27 ft
b = 99.08 ft
c² = 96.27² + 99.08² - 2 × 96.27 × 99.08 cos 77°
c² = 9267.9129 + 9816.8464 - 19076.8632 cos 77°
c² = 19084.7593 - 19076.8632 × 0.22495105434
c² = 19084.7593 - 4291.36049041
c² = 14793.398810
square root both sides
c = √14793.398810
c = 121.628116856
c ≈ 121. 63 ft
length of the zip line = 121. 63 ft
Factor and find commmon ones
25=1*5*5
33=1*3*11
GCF=1
(I am noticing that GCF=1 for many of your questions)
The answer is : 12 - all your doing is just adding five and ten then subtract 3
Let the speed of one rider = x
The speed of the second rider would e 2x ( twice as fast)
The total speed of the two riders would be x + 2x = 3x
Speed = Distance / time
Using the numbers:
3x = 72/3
Simplify:
3x = 24
Divide both sides by 3:
x = 8
The speed of one rider is 8 miles per hour
The speed of the second rider is 2(8) = 16 miles per hour.
Answer:
i guess its b and d
Step-by-step explanation:
-2+2=0
