At Castle Trigon, they are trying to determine how far the catapult is away from the tower at point A. Two soldiers using angle measuring devices determined that the angle at point B was 80° and that the angle at point A was 70°. If the two soldier stationed at points A and B are exatly 110 feet away from each other, how far is it from the catapult (point C) to the Tower at Point A?

216.7

Step-by-step explanation:

Use the Law of Sine Formula:

a/SinA = b/SinB = c/SinC

You are looking for side "b" in this case

Add up the Angles first so you can get Angle C:

180 - (80+70) = 30

After you get that, you have all your needed information to find "b":

b/Sin80 = 110/Sin30

Cross multiply and you will get:

b . Sin30 = 110 . Sin80

b = (110 . Sin80)/Sin30

Enter that into your calculator and you will get "216.7"

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."

right

step-by-step explanation: