A guide wire for a palm tree makes a 32°angle with the ground and is staked 6 feet from the base of the tree. What is the length
, to the nearest tenth of a foot, of the guide wire from the ground to the palm tree? A. 7.1, B. 8.5, C. 9.6, D. 11.3
2 answers:
Answer:
Answer is 9.6
Step-by-step explanation:
From the illustration above. See attachment for interpretation of this illustration.
To find the part label a in the attachment which is the length of the foot of the guide wire from the ground to the palm tree, we apply the sine rule, which says
a/sineA = b/sineB
In this case
a = ? , A = 58° , b = 6ft, B = 32°
So
a/sine58 = 6/sine32
a/0.848 = 6/0.5299
a = 6*0.848/0.5299
a = 5.088/0.5299
a = 9.601 ~ 9.6
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We know, opposite sides are parallelogram is parallel, therefore slopes are equal.
Slope of line one :
So, equation of other line passing through (-4,5) and have slope of -0.5 is :
y-5 = -0.5( x-(-4))
y-5 = -0.5x - 2
y + 1/2x = 3
2y + x = 6
Therefore, equation of line containing the (-4, 5) is 2y + x = 6.
Hence, this is the required solution.