Answer:
B = 48.7°, C = 61.3°, b = 12.0
Step-by-step explanation:
A triangle solver makes short work of this. (See below.)
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If you're interested in solving this using only calculator trig functions (and not the solver function), you can use the Law of Sines:
sin(C)/c = sin(A)/a
sin(C) = (c/a)sin(A)
C = arcsin(c/a·sin(A)) = arcsin(14/15·sin(70°))
C ≈ 61.3°
From the sum of angles, the third angle is ...
B = 180° -A -C = 180° -70° -61.3°
B = 48.7°
Again from the Law of Sines:
b/sin(B) = a/sin(A)
b = a·sin(B)/sin(A) = 15·sin(48.7°)/sin(70°)
b ≈ 12.0
Answer:
![\large\boxed{\left(\dfrac{5}{8},\ 12\dfrac{1}{4}\right)}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%5Cleft%28%5Cdfrac%7B5%7D%7B8%7D%2C%5C%2012%5Cdfrac%7B1%7D%7B4%7D%5Cright%29%7D)
Step-by-step explanation:
![y=ax^2bx+c\\\\(h,\ k)-vertex\\\\h=\dfrac{-b}{2a}\\\\k=\dfrac{-(b^2-4ac)}{4a}\\---------------\\\text{We have}\\\\h=-16t^2+20t+6\\\\a=-16,\ b=20,\ c=6\\\\h=\dfrac{-20}{2(-16)}=\dfrac{-20}{-32}=\dfrac{20:4}{32:4}=\dfrac{5}{8}\\\\k=\dfrac{-(20^2-4(-16)(6))}{4(-16)}=\dfrac{-(400+384)}{-64}=\dfrac{784}{64}=12\dfrac{1}{4}\\\\\text{The vertex}\ \left(\dfrac{5}{8},\ 12\dfrac{1}{4}\right)](https://tex.z-dn.net/?f=y%3Dax%5E2bx%2Bc%5C%5C%5C%5C%28h%2C%5C%20k%29-vertex%5C%5C%5C%5Ch%3D%5Cdfrac%7B-b%7D%7B2a%7D%5C%5C%5C%5Ck%3D%5Cdfrac%7B-%28b%5E2-4ac%29%7D%7B4a%7D%5C%5C---------------%5C%5C%5Ctext%7BWe%20have%7D%5C%5C%5C%5Ch%3D-16t%5E2%2B20t%2B6%5C%5C%5C%5Ca%3D-16%2C%5C%20b%3D20%2C%5C%20c%3D6%5C%5C%5C%5Ch%3D%5Cdfrac%7B-20%7D%7B2%28-16%29%7D%3D%5Cdfrac%7B-20%7D%7B-32%7D%3D%5Cdfrac%7B20%3A4%7D%7B32%3A4%7D%3D%5Cdfrac%7B5%7D%7B8%7D%5C%5C%5C%5Ck%3D%5Cdfrac%7B-%2820%5E2-4%28-16%29%286%29%29%7D%7B4%28-16%29%7D%3D%5Cdfrac%7B-%28400%2B384%29%7D%7B-64%7D%3D%5Cdfrac%7B784%7D%7B64%7D%3D12%5Cdfrac%7B1%7D%7B4%7D%5C%5C%5C%5C%5Ctext%7BThe%20vertex%7D%5C%20%5Cleft%28%5Cdfrac%7B5%7D%7B8%7D%2C%5C%2012%5Cdfrac%7B1%7D%7B4%7D%5Cright%29)
An integer is a whole number. Two integers are opposite if they have the same distance away from zero. For example,
2 and -2
or
28 and -28
Those are all integers and opposites.
Hope this helps :)
On a graph, the point moves down 9 points and to the right by 2