Problem 27 asks: In which quadrant does angle $y$ lie if $\tan y$ is positive and $\sin y$ is negative? Problem 28 asks: A right pyramid has a rectangular base with dimensions 9 cm by 5 cm. If the volume of the pyramid is 105 $cm^3$, what is the height of the pyramid?

1. Problem Description

Problem 27 asks: In which quadrant does angle $y$ lie if $\tan y$ is positive and $\sin y$ is negative?

Problem 28 asks: A right pyramid has a rectangular base with dimensions 9 cm by 5 cm. If the volume of the pyramid is 105 $cm^3$, what is the height of the pyramid?

2. Solution Steps

Problem 27:

We need to determine the quadrant in which $\tan y > 0$ and $\sin y < 0$.

* Quadrant I: $\sin y > 0$, $\cos y > 0$, $\tan y > 0$

* Quadrant II: $\sin y > 0$, $\cos y < 0$, $\tan y < 0$

* Quadrant III: $\sin y < 0$, $\cos y < 0$, $\tan y > 0$

* Quadrant IV: $\sin y < 0$, $\cos y > 0$, $\tan y < 0$

Therefore, $y$ must lie in Quadrant III.

Problem 28:

The volume of a pyramid is given by:

$V = \frac{1}{3}Bh$

where $V$ is the volume, $B$ is the area of the base, and $h$ is the height.

In this case, the base is a rectangle with dimensions 9 cm by 5 cm. Thus, the area of the base is:

$B = 9 \times 5 = 45$ $cm^2$

We are given that the volume is 105 $cm^3$. We can now solve for the height $h$:

$105 = \frac{1}{3}(45)h$

$105 = 15h$

$h = \frac{105}{15} = 7$ cm

3. Final Answer

Problem 27: C. Third only

Problem 28: D. 7 cm