A kite is flying 70 feet above the ground and is attached to a string tied to a stake on the ground. The angle of elevation form
ed by the string and the ground is 40°. Find the length of the string to the nearest foot.
2 answers:
Answer:
94 feet.
Step-by-step explanation:
The angle of elevation is the angle made by the eye of the observer and the ground level. In this instance, it is the angle formed by the string and the ground which is 40°.
From the attached diagram, the length of the string is x and the height above the ground is 70 feet. These two sides are the hypotenuse and the opposite sides respectively
Using SOH CAH TOA
Sin 40 = 70/x
x = 70/sin 40
x = 93.95 feet.
The length of the string to the nearest foot is 94 feet.
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Answer:
29% of the drive
Step-by-step explanation:
The plot of the problem is:
Transmitter at origin (0,0)
City to the north at (0,70)
City to the east at (74,0)
The path from city to city is a line with slope:
m = (-70)/74 = -35/37
and y-intercept at y = 70, so the equation is y = (-35/37)*x + 70.
The transmitter reach the area enclosed by the next circle:
x^2 + y^2 = 53^2
See the picture attached
The intersection is gotten from the picture or solving:
x^2 + [(-35/37)*x + 70]^2 = 53^2
the points approximately are: (24.1, 47.2) and (45.8, 26.7)
From Pythagorean theorem the total distance of the trip is:
d1 = √(70^2 + 74^2) ≈ 101.9 miles
And the distance when the signal is picked up is:
d2 =√ [(45.8 - 24.1)^2 + (47.2 - 26.7)^2] ≈ 29.9 miles
You will pick up a signal from the transmitter in (d2/d1)*100 = 29% of the drive.
