David Weber, Talei Kunkel, Rose Harrison and, Fatima Remtulla Solutions for Chapter: Triangles Principles, Processes and Solutions, Exercise 33: Unit review

During a solar eclipse,the moon passes between the sun and earth and covers sun almost entirely despite being considerably smaller.Why the moon covers almost all of the sun during an eclipse.

A television manufacturer  made the following claim in an advertisement,
Our $80 inch$  AQUOS TV delivers more than double the screen area of a $55 inch$ TV for an amazing viewing experience.Show that,80 inch  TV delivers more than double the screen area of a $55 inch$.

A television manufacturer  made the following claim in an advertisement,
Our $80 inch$  AQUOS TV delivers more than double the screen area of a $55 inch$ TV for an amazing viewing experience.Show that this claim is true even if both television have aspect ratio of $16:9$.(Aspect ratio is $length:width$)

In order to describe the location of celestial bodies astronomers used a three-dimensional coordinate system,with our sun at the origin $\left(0,0,0\right)$,all other objects are given a coordinate in the form of $\left(x,y,z\right)$.Write down the distance formula for the pair of  three-dimensional coordinate.

In order to describe the location of celestial bodies astronomers used a three-dimensional coordinate system,with our sun at the origin $\left(0,0,0\right)$.Find the distance between Sun and Polaris $\left(99.6,28.2,376.0\right)$.

In order to describe the location of celestial bodies astronomers used a three-dimensional coordinate system,with our sun at the origin $\left(0,0,0\right)$.Find the distance between Sun and Alpha centauri $\left(-1.8,0.0,3.9\right)$.

In order to describe the location of celestial bodies astronomers used a three-dimensional coordinate system,with our sun at the origin $\left(0,0,0\right)$.Find the distance between Sun and Sirius $\left(-3.4,-3.1,7.3\right)$.

In order to describe the location of celestial bodies astronomers used a three-dimensional coordinate system,with our sun at the origin $\left(0,0,0\right)$.Coordinates of Polaris $\left(99.6,28.2,376.0\right)$ and Alpha Centauri $\left(-1.8,0.0,3.9\right)$.Find the distance between Polaris and Alpha Centauri.