a) How king is the zip-line?
The zip-line is 371.1 ft long
The zip-line, the 150 foot pole and the distance from the 5 foot stake to the 150 foot pole all form a right-angled triangle.
The right-angled triangle with hypotenuse side, h the zip-line, adjacent side, x the distance from the 5 foot stake to the 150 foot pole and opposite side, y the distance from the top of the stake to the platform, since the angle of elevation of the platform from the stake is 23°.
Using trigonometric ratios,
sin23° = y/h
h = y/sin23°
y = 150 ft - 5 ft = 145 ft
So, h = 145 ft/sin23°
h = 145 ft/0.3907
h = 371.1 ft
So, the zip-line is 371.1 ft long
b) How far is the stake from the pole?
The stake is 341.6 ft far from the pole.
Also, since the zip-line, the 150 foot pole and the distance from the 5 foot stake to the 150 foot pole all form a right-angled triangle.
The right-angled triangle with hypotenuse side, h the zip-line, adjacent side, x the distance from the 5 foot stake to the 150 foot pole and opposite side, y the distance from the top of the stake to the platform, since the angle of elevation of the platform from the stake is 23°.
Using trigonometric ratios,
tan23° = y/x
y = 150 ft - 5 ft = 145 ft
So, x = y/tan23°
x = 145 ft/0.4245
x = 341.6 ft
So, the stake is 341.6 ft far from the pole.
Learn more about angle of elevation here:
https://brainly.com/question/21095259
