Answer:
all i see it dots
Step-by-step explanation:
Answer:
0
1
Step-by-step explanation:
First question:
You are given a side, a, and its opposite angle, A. You are also given side b. Use that in the law of sines and solve for the other angle, B.
![\dfrac{a}{\sin A} = \dfrac{b}{\sin B}](https://tex.z-dn.net/?f=%20%5Cdfrac%7Ba%7D%7B%5Csin%20A%7D%20%3D%20%5Cdfrac%7Bb%7D%7B%5Csin%20B%7D%20)
![\dfrac{10}{\sin 30^\circ} = \dfrac{40}{\sin B}](https://tex.z-dn.net/?f=%20%5Cdfrac%7B10%7D%7B%5Csin%2030%5E%5Ccirc%7D%20%3D%20%5Cdfrac%7B40%7D%7B%5Csin%20B%7D%20)
![\dfrac{1}{0.5} = \dfrac{4}{\sin B}](https://tex.z-dn.net/?f=%20%5Cdfrac%7B1%7D%7B0.5%7D%20%3D%20%5Cdfrac%7B4%7D%7B%5Csin%20B%7D%20)
![\sin B = 2](https://tex.z-dn.net/?f=%20%5Csin%20B%20%3D%202%20)
The sine function can never equal 2, so there is no triangle in this case.
Answer: no triangle
Second question:
You are given a side, b, and its opposite angle, B. You are also given side c. Use that in the law of sines and solve for the other angle, C.
![\dfrac{b}{\sin B} = \dfrac{c}{\sin C}](https://tex.z-dn.net/?f=%20%5Cdfrac%7Bb%7D%7B%5Csin%20B%7D%20%3D%20%5Cdfrac%7Bc%7D%7B%5Csin%20C%7D%20)
![\dfrac{10}{\sin 63^\circ} = \dfrac{}{\sin C}](https://tex.z-dn.net/?f=%20%5Cdfrac%7B10%7D%7B%5Csin%2063%5E%5Ccirc%7D%20%3D%20%5Cdfrac%7B%7D%7B%5Csin%20C%7D%20)
![\sin C = \dfrac{8.9\sin 63^\circ}{10}](https://tex.z-dn.net/?f=%20%5Csin%20C%20%3D%20%5Cdfrac%7B8.9%5Csin%2063%5E%5Ccirc%7D%7B10%7D%20)
![C = \sin^{-1} \dfrac{8.9\sin 63^\circ}{10}](https://tex.z-dn.net/?f=%20C%20%3D%20%5Csin%5E%7B-1%7D%20%5Cdfrac%7B8.9%5Csin%2063%5E%5Ccirc%7D%7B10%7D%20)
![C \approx 52.5^\circ](https://tex.z-dn.net/?f=%20C%20%5Capprox%2052.5%5E%5Ccirc%20)
One triangle exists for sure. Now we see if there is a second one.
Now we look at the supplement of angle C.
m<C = 52.5°
supplement of angle C: m<C' = 180° - 52.5° = 127.5°
We add the measures of angles B and the supplement of angle C:
m<B + m<C' = 63° + 127.5° = 190.5°
Since the sum of the measures of these two angles is already more than 180°, the supplement of angle C cannot be an angle of the triangle.
Answer: one triangle
Answer:
B
Step-by-step explanation:
![f(7)=\sqrt{7^2+8*7}=\sqrt{49+56}=\sqrt{105} \approx 10.247\\f(8)=\sqrt{8^2+8*8}=\sqrt{128}=8\sqrt{2} \approx 11.314\\f(8)-f(7)=11.314-10.247=1.067 \approx 1.07](https://tex.z-dn.net/?f=f%287%29%3D%5Csqrt%7B7%5E2%2B8%2A7%7D%3D%5Csqrt%7B49%2B56%7D%3D%5Csqrt%7B105%7D%20%5Capprox%2010.247%5C%5Cf%288%29%3D%5Csqrt%7B8%5E2%2B8%2A8%7D%3D%5Csqrt%7B128%7D%3D8%5Csqrt%7B2%7D%20%5Capprox%2011.314%5C%5Cf%288%29-f%287%29%3D11.314-10.247%3D1.067%20%5Capprox%201.07)