Answer:
a= 120
b= 60
Step-by-step explanation:
This is what I was able to come up with. Hope I was able to help
Answer:
see attached
Step-by-step explanation:
![tan \frac{x}{2} =\pm \sqrt{\frac{1-cos x}{1+cos x}}](https://tex.z-dn.net/?f=tan%20%5Cfrac%7Bx%7D%7B2%7D%20%3D%5Cpm%20%5Csqrt%7B%5Cfrac%7B1-cos%20x%7D%7B1%2Bcos%20x%7D%7D)
Find cos using trig identities:
![sec x = \frac{1}{cos x} \\ tan^2 x = sec^2 x -1](https://tex.z-dn.net/?f=sec%20x%20%3D%20%5Cfrac%7B1%7D%7Bcos%20x%7D%20%20%5C%5C%20tan%5E2%20x%20%3D%20sec%5E2%20x%20-1)
Therefore
![cos x = \frac{1}{sec x} =\pm \frac{1}{\sqrt{tan^2 x +1}}](https://tex.z-dn.net/?f=cos%20x%20%3D%20%5Cfrac%7B1%7D%7Bsec%20x%7D%20%3D%5Cpm%20%5Cfrac%7B1%7D%7B%5Csqrt%7Btan%5E2%20x%20%2B1%7D%7D)
Sub in tan x = 3, (Note that x is in 3rd quadrant, cos x < 0)
![cos x =- \frac{1}{\sqrt{3^2 +1}} = -\frac{1}{\sqrt{10}}](https://tex.z-dn.net/?f=cos%20x%20%3D-%20%5Cfrac%7B1%7D%7B%5Csqrt%7B3%5E2%20%2B1%7D%7D%20%3D%20-%5Cfrac%7B1%7D%7B%5Csqrt%7B10%7D%7D)
Finally, sub into Half-angle formula:(Note x/2 is in 2nd quadrant, tan x<0)
Answer:
![b < 9](https://tex.z-dn.net/?f=b%20%3C%209)
Step-by-step explanation:
We are given the following in the question:
Height of triangle,h = 4 inches
Area of triangle =
![A = \dfrac{1}{2}\times b\times h](https://tex.z-dn.net/?f=A%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%20b%5Ctimes%20h)
where b is the base of the triangle and h is the height of the triangle.
The area of the triangular sign must be less than 18 square inches.
Thus, we can write the inequality:
![A< 18\\\\\Rightarrow \dfrac{1}{2}\times b \times h < 18\\\\\Rightarrow b < \dfrac{18\times 2}{4}\\\\\Rightarrow b < 9](https://tex.z-dn.net/?f=A%3C%2018%5C%5C%5C%5C%5CRightarrow%20%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%20b%20%5Ctimes%20h%20%3C%2018%5C%5C%5C%5C%5CRightarrow%20b%20%3C%20%5Cdfrac%7B18%5Ctimes%202%7D%7B4%7D%5C%5C%5C%5C%5CRightarrow%20b%20%3C%209)
The above inequality is the required inequality that describes the possible base length of the triangular sign.