Question 1

The figure shows $ \Delta ABC \sim \Delta DEF$ with side lengths as indicated. 
What is the value of $x$?
Enter your answer in the box.

(*NO CALCULATOR*)

Accepted Answer

15

Question 2

In this figure, triangle $GHJ$ is similar to triangle $PQR$.
Based on this information, which ratio represents $tanH$?

(*NO CALCULATOR*)

Accepted Answer

$\frac{8}{15}$

Answer

$\frac{8}{17}$

Answer

$\frac{17}{8}$

Answer

$\frac{15}{8}$

Question 3

A spring is attached at one end to support $B$ and at the other end to collar $A$, as represented in the figure. Collar $A$ slides along the vertical bar between points $C$ and $D$. In the figure, the angle $	heta$ is the angle created as the collar moves between points $C$ and $D$.

When $	heta = 28 \degree$, what is the distance from point $A$ to point $B$ to the nearest tenth of a foot?
Enter your answer in the box.

Accepted Answer

3.4

Question 4

A spring is attached at one end to support $B$ and at the other end to collar $A$, as represented in the figure. Collar $A$ slides along the vertical bar between points $C$ and $D$. In the figure, the angle $	heta$ is the angle created as the collar moves between points $C$ and $D$.

When the spring is stretched and the distance from point $A$ to point $B$ is 5.2 feet, what is the value of $	heta$ to the nearest tenth of a degree?

Accepted Answer

$54.8 \degree$

Answer

$60.0 \degree$

Answer

$35.2 \degree$

Answer

$45.1 \degree$

Question 5

The figure shows two semicircles with centers $P$ and $M$. The semicircles are tangent to each other at point $B$, and $\stackrel \longrightarrow {DE}$ is tangent to both semicircles at $F$ and $E$.

If $PB = BC = 6$, what is $ED$?

Accepted Answer

$\sqrt{72}$

Answer

$\sqrt{48}$

Answer

8

Answer

6

Question 6

In the $xy$-coordinate plane, $\Delta ABC$ has vertices $A(-4, 6), 8(2, 6)$, and $C(2, 2)$. $\Delta DEF$ is shown in the plane. 
What is the scale factor and the center of dilation that maps $\Delta ABC$ to $\Delta DEF$?

Accepted Answer

The scale factor is $\frac{1}{2}$, and the center of dilation is the origin.

Answer

The scale factor is $\frac{1}{2}$, and the center of dilation is point $B$.

Answer

The scale factor is 2, and the center of dilation is the origin.

Answer

The scale factor is 2, and the center of dilation is point $B$.

Question 7

Mariela is standing in a building and looking out of a window at a tree. The tree is 20 feet away from Mariela. Mariela's line of sight to the top of the tree creates a $42 \degree$ angle of elevation, and her line of sight to the base of the tree creates a $31\degree$  angle of depression. 
What is the height, in feet, of the tree?
Enter your answer in the box.

Accepted Answer

freetextm://30:30.03

Question 8

In right triangle $ABC$, $m\angle B 
eq m\angle C$. Let $sinB = r$ and $cosB = s$. What is $sinC - cosC$?

Accepted Answer

$s-r$

Answer

$\frac{r}{s}$

Answer

$r-s$

Answer

$r+s$

Question 9

Line segment $AB$ with endpoints $A(4, 16)$ and $8(20, 4)$ lies in the coordinate plane. The segment will be dilated with a scale factor of $\frac{3}{4}$ and a center at the origin to create $\overline{A'B'}$. What will be the length of $\overline{A'B'}$?

Accepted Answer

15

Answer

12

Answer

4

Answer

5

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