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
Answer:
the amount of matter is mass. how much space you take up
Step-by-step explanation:
Answer:
A triangle with two congruent sides and two congruent angles ( base Angles) is called isosceles triangle.
Answer: The second option (160 cm)
Step-by-step explanation:
1. You can obtain the perimeter of a quadrilateral by adding the lenghts of the sides.
2. You know that the ratio of the side lengths is 3:3:5:8 and the perimeter is 380 centimeters.
3. Therefore, you can write the following expression, where x is an integer:
4. Solve for x:
5. Therefore, the longest side is:
(160 cm)
