In triangle ABC, AP is an angle bisector of angle BAC. What is the length of PC? Round you answer to the nearest whole number.
2 answers:
Answer:
D
Step-by-step explanation:
the angle bisector divides the opposite side into segments that are proportional to the other 2 sides.
note that BP = 16 - PC , then
=
( substitute values )
=
=
( cross- multiply )
4 PC = 5(16 - PC) ← distribute parenthesis
4 PC = 80 - 5 PC ( add 5 PC to both sides )
9 PC = 80 ( divide both sides by 9 )
PC = 8.888... ≈ 9 ( to the nearest whole number )
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Remember that c is the initial height. Since we the rocket is in a 99-foot cliff, c=99. Also, we know that the velocity of the rocket is 122 ft/s; therefore v=122
Lets replace the values into the the vertical motion formula to get:
Notice that the rocket hits the ground at the bottom of the cliff, which means that the final height is 99-foot bellow its original position; therefore, our final height will be h=-99
Lets replace this into our equation to get:
Now we can apply the quadratic formula
where a=-16, b=122, and c=198
or 
or 
or 
Since the time can't be negative, we can conclude that the rocket hits the ground after 9 seconds.
Lets replace the values into the the vertical motion formula to get:
Notice that the rocket hits the ground at the bottom of the cliff, which means that the final height is 99-foot bellow its original position; therefore, our final height will be h=-99
Lets replace this into our equation to get:
Now we can apply the quadratic formula
Since the time can't be negative, we can conclude that the rocket hits the ground after 9 seconds.