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yialefi
11.10.2019 •
Mathematics
You want to measure the height of a tree growing vertically on the side of a hill. the hill makes an angle of 20°with the horizontal. standing 15ft. downhill from the base of the tree, you measure the angle formed by the hill and the top of the tree to be 45°. find the height of the tree to the nearest foot. show your work.
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Ответ:
Solving for the variable "a" which is base of downhill to the tree, we have it:
cos 20° = a / 15 ft
a = 15*cos 20°
a = 14.095 feet
Solving for the variable "x" which is the side of the hill to the base of the tree, we have it:
sin 20° = x / 15 ft
x = 15 * sin20°
x = 5.130 feet
Solving for the variable "y", which is the height of the tree, we have it:
tan 45° = (x+y) / a
tan 45° = (5.13 + y) / 14.095
y = 14.095*tan45° - 5.13
y = 8.965 feet
The height of the tree is 8.965 feet.
Ответ:
Let's call the distance between the moon and sun as z. The scientist can calculate the numerical value of sin x° and then write sin x° as y / z. They can then set the numerical value of sin x° equal to y / z and then solve for z.