19.941 would round to 20 when rounded to the nearest one.
Answer:
a= 121°
b=62°
c=59°
Step-by-step explanation:
I first found b because they are vertical angles
Because I know the measure of angle b I take 180 (total sum of a triangle) and subtracted 62 from 180 which gave me 59 and because both base angles are equal to each other I divided 118 by 2 which gave me 59. Giving me the measure of angle c.
By adding angles b and c they would give me the measure of angle a.
__________________________________________________________Hope this helps!!
If I am wrong, please tell me, I enjoy learning from my mistakes:)
Answer:
![\sqrt{2} -1](https://tex.z-dn.net/?f=%5Csqrt%7B2%7D%20-1)
Step-by-step explanation:
22.5 degrees is half of 45 degrees (special angle for which we know exactly the value of all three basic trigonometric functions (sine, cosine, and tangent).
So we start recalling the formula for tangent of a half angle: ![tan(\frac{\alpha }{2} )= \frac{1-cos(\alpha) }{sin(\alpha) }](https://tex.z-dn.net/?f=tan%28%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%29%3D%20%5Cfrac%7B1-cos%28%5Calpha%29%20%7D%7Bsin%28%5Calpha%29%20%7D)
We need just the values of:
![sin(\alpha )=sin(45^o)=\frac{\sqrt{2} }{2}](https://tex.z-dn.net/?f=sin%28%5Calpha%20%29%3Dsin%2845%5Eo%29%3D%5Cfrac%7B%5Csqrt%7B2%7D%20%7D%7B2%7D)
and of
![cos(\alpha )=cos(45^o)=\frac{\sqrt{2} }{2}](https://tex.z-dn.net/?f=cos%28%5Calpha%20%29%3Dcos%2845%5Eo%29%3D%5Cfrac%7B%5Csqrt%7B2%7D%20%7D%7B2%7D)
to answer the question. Then, we use those values in the original formula for tangent of a half angle:
![tan(\frac{\alpha }{2} )= \frac{1-cos(\alpha) }{sin(\alpha) }\\tan(22.5^o)=\frac{1-\frac{\sqrt{2} }{2} }{\frac{\sqrt{2} }{2}} =\frac{2-\sqrt{2} }{\sqrt{2} } =\frac{2\sqrt{2}-2 }{2} =\sqrt{2} -1](https://tex.z-dn.net/?f=tan%28%5Cfrac%7B%5Calpha%20%7D%7B2%7D%20%29%3D%20%5Cfrac%7B1-cos%28%5Calpha%29%20%7D%7Bsin%28%5Calpha%29%20%7D%5C%5Ctan%2822.5%5Eo%29%3D%5Cfrac%7B1-%5Cfrac%7B%5Csqrt%7B2%7D%20%7D%7B2%7D%20%7D%7B%5Cfrac%7B%5Csqrt%7B2%7D%20%7D%7B2%7D%7D%20%3D%5Cfrac%7B2-%5Csqrt%7B2%7D%20%7D%7B%5Csqrt%7B2%7D%20%7D%20%3D%5Cfrac%7B2%5Csqrt%7B2%7D-2%20%7D%7B2%7D%20%3D%5Csqrt%7B2%7D%20-1)