A guy wire supports a tower. The wire forms an angle of 57 degrees with level ground. The wire is anchored to the ground 16.5m away from the base of the tower.
a)How high is the tower?
B) how long is the guy wire?
2006-08-02 08:03:40 · 9 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
A)Opposite/16.5 = tan 57 => opp = height = 25.4m
B)16.5/hypotenuse = cos 57 => hyp = length of wire= 30.3 m
2006-08-02 08:10:42 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Imagine this situation as a triangle
The wire is the hypotenuse, because it makes the angle with the ground
The ground is the adjacent leg, since it is near the angle.
The tower is the opposite leg, because it is opposite the angle the wire makes with the ground.
So you get:
theta = 57degrees;
opp. = y
adj. = x = 16.5 m
hyp = r
The ratios are
sin (theta) = y/r
cos (theta) = x/r
tan (theta) = y/x
a)"How high is the tower " means find "y"
you know theta and "x", so use the tan ratio:
tan (57) = y/16.5
y = 16.5 tan(57) = 25.4m
The tower is 25.4 meters
B) "how long is the guy wire" means find "r"
Knowing theta, "x" and "y", use cos or sin:
sin (57) = 25.4/r ----> r = 25.4 / sin (57) = 30.3m
cos (57) = 16.5/r ----> r = 16.5 / cos (57) = 30.3m
The wire is 30.3 meters
2006-08-02 15:47:15 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Height of tower=25.467m
Length of wire=30.295m
2006-08-02 15:13:10 · answer #3 · answered by t_d_bauer 3 · 0⤊ 0⤋
Remember the famous mathematician, Soh-Cah-Toa:
Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent
2006-08-02 18:23:03 · answer #4 · answered by Kevin B 2 · 0⤊ 0⤋
the height of the tower is 16.5*tan57=25.408m
So, the length of the wire is 25.408/sin57=30.2953m
2006-08-02 15:12:41 · answer #5 · answered by sharanan 2 · 0⤊ 0⤋
a) 16.5 * tan 57deg = height of tower
b) 16.5 / cos 57deg = length of guide wire
2006-08-02 15:10:49 · answer #6 · answered by Anonymous · 0⤊ 0⤋
(a)height=16.5 tan 57* =25.41m
(b)guy wire is 16.5 sec 57* =30.30
2006-08-02 15:10:54 · answer #7 · answered by raj 7 · 0⤊ 0⤋
tan(57) = (opposite)/16.5
tan(57) = y/(16.5)
y = (16.5)tan(57)
y = (33tan(57))/2
cos(57) = (16.5)/hypothenuse
cos(57) = (16.5)/x
x = (16.5)/(cos(57))
a.)
the tower is about 25.4 meters high
b.)
The guy wire is about 30.3 meters long
2006-08-02 16:26:51 · answer #8 · answered by Sherman81 6 · 0⤊ 0⤋
I would help you except I forgot how to do them, sorry. ): I think I need to review my math.
2006-08-02 15:10:18 · answer #9 · answered by Jina 4 · 0⤊ 0⤋