Answer:
74
Step-by-step explanation:
180-80-26=74
1560 cm^2 as you subtract the small prism from the large
Answer:
ASA
Step-by-step explanation:
Triangle ABD is congruent to triangle BDC by ASA because angle B in ABD is 30 degrees. Then they give you BD which equals BD by the reflexive property. And finally angle D in ABD is also 30 degrees. In triangle BCD, angle B is 30 degrees, BD = BD, and angle D in BCD is 30 degress. So we have an angle (B), side (BD), and another angle (D)
It depends on how big the countertop is. :)
Answer:
The angle between the given vectors u and v is ![\theta=cos^{-1}\left[\frac{3}{\sqrt{10}}\right]](https://tex.z-dn.net/?f=%5Ctheta%3Dcos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B3%7D%7B%5Csqrt%7B10%7D%7D%5Cright%5D)
Step-by-step explanation:
Given vectors are
and 
Now compute the dot product of u and v:




Now find the magnitude of u and v:









To find the angle between the given vectors

![\theta=cos^{-1}\left[\frac{\overrightarrow{u}.\overrightarrow{v}}{|\overrightarrow{u}|\overrightarrow{v}|}\right]](https://tex.z-dn.net/?f=%5Ctheta%3Dcos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B%5Coverrightarrow%7Bu%7D.%5Coverrightarrow%7Bv%7D%7D%7B%7C%5Coverrightarrow%7Bu%7D%7C%5Coverrightarrow%7Bv%7D%7C%7D%5Cright%5D)
![=cos^{-1}\left[\frac{15}{5\times \sqrt{10}}\right]](https://tex.z-dn.net/?f=%3Dcos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B15%7D%7B5%5Ctimes%20%5Csqrt%7B10%7D%7D%5Cright%5D)
![=cos^{-1}\left[\frac{15}{5\times \sqrt{10}}\right]](https://tex.z-dn.net/?f=%3Dcos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B15%7D%7B5%5Ctimes%20%5Csqrt%7B10%7D%7D%5Cright%5D)
![\theta=cos^{-1}\left[\frac{3}{\sqrt{10}}\right]](https://tex.z-dn.net/?f=%5Ctheta%3Dcos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B3%7D%7B%5Csqrt%7B10%7D%7D%5Cright%5D)
Therefore the angle between the vectors u and v is
![\theta=cos^{-1}\left[\frac{3}{\sqrt{10}}\right]](https://tex.z-dn.net/?f=%5Ctheta%3Dcos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B3%7D%7B%5Csqrt%7B10%7D%7D%5Cright%5D)