A 15-foot flagpole leans slightly, such that it makes an 80° angle with the ground. The shadow of the flagpole is 10 feet long w
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Answer:
m∠ MNL = 78º
Step-by-step explanation:
<u>Arcs meassures </u>
mML = (11x - 5)º
mJK = (4x + 26)°
<u>Angle meassure</u>
m∠MNL = (10 x – 12)º
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angle measure = average of arcs
m∠MNL = (mML+ mJK)/2
Replacing
(10x – 12)º = ((11x - 5)º + (4x + 26)° )/ 2
10x -12 = (15x + 21 )/2
10x - 7.5x = 10.5 + 12
2.5x = 22.5
x= 9
m∠MNL = (10 x – 12)º
= 90 - 12
= 78º
Using Pythagoras theorem, the top of the ladder moving down when the foot of the ladder is 3 feet from the wall is of -0.518 feet/sec.
Let distance from the wall to the foot of the ladder is 'x' feet and the height of the top of the ladder is 'y' feet.
Pythagoras theorem, --->(1)
Given, at x=3
Put x=3 in Pythagoras theorem equation (1)
= 135
y = 11.61
Derive equation (1) w.r.t to 't'
---->(2)
substitute the value of 'x', 'dx/dt' and 'y' in equation (2), we get the fast of the top of the ladder moving down when the foot of the ladder is 3 feet from the wall
12 + 23.22 = 0
Hence, using Pythagoras theorem the top of the ladder moving down when the foot of the ladder is 3 feet from the wall is of -0.518 feet/sec.
Learn more about Pythagoras theorem here
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