Answer:
![28.07^{\circ}](https://tex.z-dn.net/?f=28.07%5E%7B%5Ccirc%7D)
Step-by-step explanation:
We can use basic trig. for a right triangle to solve this problem. In any right triangle, the tangent of an angle is equal to its opposite side divided by the hypotenuse (longest side) of the triangle.
The right triangle we're looking at involves the two dotted lines and an edge of the prism.
The bottom dotted line is a diagonal of the rectangular base of the prism. We can use the Pythagorean Theorem to find its length.
The Pythagorean Theorem states that for any right triangle,
, where
and
are the two legs of the triangle and
is the hypotenuse.
In this case, the two legs are 9 and 12 and we are solving for
:
![9^2+12^2=c^2,\\81+144=c^2,\\225=c^2,\\c=15](https://tex.z-dn.net/?f=9%5E2%2B12%5E2%3Dc%5E2%2C%5C%5C81%2B144%3Dc%5E2%2C%5C%5C225%3Dc%5E2%2C%5C%5Cc%3D15)
This is theta's adjacent side. Its opposite side is an edge of the prism labelled as 8 inches. Therefore, we have the following equation:
![\tan \theta = \frac{8}{15}](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%20%3D%20%5Cfrac%7B8%7D%7B15%7D)
Take the inverse tangent of both sides:
![\arctan(\tan \theta)=\arctan(\frac{8}{15})](https://tex.z-dn.net/?f=%5Carctan%28%5Ctan%20%5Ctheta%29%3D%5Carctan%28%5Cfrac%7B8%7D%7B15%7D%29)
Simplify using
:
![\theta=\arctan(\frac{8}{15}),\\\theta=28.07248694\approx \boxed{28.07^{\circ}}](https://tex.z-dn.net/?f=%5Ctheta%3D%5Carctan%28%5Cfrac%7B8%7D%7B15%7D%29%2C%5C%5C%5Ctheta%3D28.07248694%5Capprox%20%5Cboxed%7B28.07%5E%7B%5Ccirc%7D%7D)
The opportunity cost that Ann is going to have if she buys the pair of jeans is the chance to buy the pair of shoes with her allowance. She exchanged her opportunity of buying the shoes by buying the pair of jeans. This is the opportunity cost because the potential of losing the alternative (shoes) happened by purchasing the other.
Answer: 16
Step-by-step explanation:
Every number next to the variable will be the coefficient in all algebraic expressions.
10% of 650 visitors is:
650 visitors* (10/100)= 65 visitors.
650 visitors+ 65 visitors= 715 visitors.
There are 715 visitors on Saturday~