What is x? mo is an angle bisector
2 answers:
Answer: The correct option is (D) 24.
Step-by-step explanation: We are given to find the value of x from the given figure, where MO is an angle bisector.
From the figure, we note that
MO is the angle bisector of angle M in ΔLMN, where
ML = x cm, MN = 12 cm, LO = 41 cm and ON = 7 cm.
We have the following theorem :
<u><em>Angle bisector theorem </em></u>: An angle bisector of a triangle will divide the opposite side into two segments that are proportional to the other two sides of the triangle.
Applying the above theorem in the given triangle LMN, we have
Thus, the required value of x is 24.
Option (D) is CORRECT.
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Answer:
1,809.98 lb*m/s^2
Step-by-step explanation:
First, we want to know how much weight of the boulder is projected along the path in which the boulder can move.
The weight of the boulder is:
W = 322lb*9.8 m/s^2 = (3,155.6 lb*m/s^2)
This weight has a direction that is vertical, pointing downwards.
Now, we know that the angle of the hill is 35°
The angle that makes the direction of the weight and this angle, is:
(90° - 35°)
(A rough sketch of this situation can be seen in the image below)
Then we need to project the weight over this direction, and that will be given by:
P = W*cos(90° - 35°) = (3,155.6 lb*m/s^2)*cos(55°) = 1,809.98 lb*m/s^2
This is the force that Samuel needs to exert on the boulder if he wants the boulder to not roll down.
