Question 1.

(05.04 MC)

If E measures 45, F measures 98, and e is 5 feet, then find f using the Law of Sines. Round your answer to the nearest foot.

triangle EFG with side e across from angle E, side f across from angle F, and side g across from angle g

4 feet

5 feet

6 feet

7 feet

Question 2

(04.02 MC)

Point A is located at (2, 2), and point M is located at (1, 0). If point M is the midpoint of segment AB, find the location of point B.

(0.5, 1)

(4, 2)

(5, 4)

(1, 1)

Question 3

(04.03 MC)

Find the perimeter of a quadrilateral with vertices at C (2, 1), D (2, 4), E (5, 0), and F (1, 3).

12 units

16 units

20 units

24 units

Question 4

(04.04 MC)

A skateboard halfpipe is being designed for a competition. The halfpipe will be in the shape of a parabola and will be positioned above the ground such that its focus is 20 ft above the ground. Using the ground as the x-axis, where should the base of the halfpipe be positioned? Which equation best describes the equation of the halfpipe?

(0, 20); y equals one over eighty times x squared plus 20

(0, 20); y equals one over eighty times x squared minus 20

(0, 10); y equals one over forty times x squared plus 10

(0, 10); y equals one over forty times x squared minus 10

Question 5

(05.02 LC)

The picture below shows a box sliding down a ramp:

A right triangle ABC has measure of angle ABC equal to 90 degrees and measure of angle ACB equal to 62 degrees. The length of AB is 10 feet.

What is the distance, in feet, that the box has to travel to move from point A to point C?

10 divided by cot 62 degrees

10 cosec 62

10 divided by sec 62 degrees

10 sin 62

Question 6

(05.01 LC)

The figure below shows a triangular piece of cloth:

Triangle ABC has angle ABC equal to 90 degrees and angle BAC equal to 35 degrees. Length of AC is 8 inches.

What is the length of the portion BC of the cloth?

8 cos 35

sin 35 degrees divided by 8

cos 35 degrees divided by 8

8 sin 35

Question 7

(04.04 MC)

Which is the equation of a hyperbola with directrices at x = 2 and foci at (5, 0) and (5, 0)?

y squared over 40 minus x squared over 10 equals 1

y squared over 10 minus x squared over 15 equals 1

x squared over 10 minus y squared over 40 equals 1

x squared over 10 minus y squared over 15 equals 1

Question 8

(04.01 MC)

Sammy is classifying quadrilateral EFGH. How can she use coordinate geometry to determine whether EFGH is a rhombus?

E(2, 5), F(1, 3), G(2, 1), H(3, 3)

Sammy can use the distance formula to show that the opposite sides have equal slopes.

Sammy can use the distance formula to show that all sides are equal.

Sammy can use the slope formula to show that the opposite sides have equal slopes.

Sammy can use the slope formula to show that all sides are equal.

Question 9

(05.03 MC)

Two boats start their journey from the same point A and travel along directions AC and AD, as shown below:

ABC is a right triangle with measure of angle ABC equal to 90 degrees and length of AB equal to 200 feet. There is a point C on BD such that measure of angle ACB is 60 degrees and measure of angle ADC is 30 degrees.

What is the distance, CD, between the boats?

230.9 ft

284.3 ft

115.5 ft

173.2 ft

Question 10

(05.01 LC)

Which pair of angles has congruent values for the sin x and the cos y?

35; 55

35; 145

35; 70

35; 35

Question 11

(04.03 MC)

A segment with endpoints A (4, 2) and C (1, 5) is partitioned by a point B such that AB and BC form a 1:3 ratio. Find B.

(1, 2.5)

(2.5, 3.5)

(3.25, 2.75)

(3.75, 4.5)

Question 12

(04.02 MC)

chose the equation of a line that passes through the point (7, 3) and is parallel to the line y = negative 2 over 3x + 3.

y = 3 over 2x 3

y = 3 over 2x + 3

y = negative 2 over 3x + 23 over 3

y = negative 2 over 3x 23 over 3

Question 13

(05.01 LC)

A lamppost, CAB, bent at point A after a storm. The tip of the lamppost touched the ground at point C, as shown below:

Triangle ABC has measure of angle C equal to 50 degrees, measure of angle ABC equal to 90 degrees, and length of BC equal to 10 feet.

What is the height, in feet, of the portion AB of the lamppost?

10 divided by tan 50 degrees

10 divided by cos 50 degrees

10 cos 50

10 tan 50

Question 14

(05.01 LC)

Use the image below to answer the following question:

A right triangle is shown. The two angles that are not 90 degrees are marked x and y. The leg across from angle y measuring 9, another leg across from angle x measuring 12, and the hypotenuse measuring 15.

What relationship do the ratios of sin y and cos x share?

The ratios are both identical. (9 over 15 and 9 over 15)

The ratios are opposites. (negative 9 over 15 and 9 over 15)

The ratios are reciprocals. (9 over 15 and 15 over 9)

The ratios are both negative. (negative 15 over 9 and negative 9 over 15)

Question 15

(05.03 MC)

The figure below shows a triangular wooden frame ABC. The side AD of the frame has rotted and needs to be replaced:

Triangle ABC has length of BC equal to 10 inches. A line segment DC joins the point D on AB with point C. Measure of angle ABC is 90 degrees, ACD is 15 degrees, and measure of angle DCB is 30 degrees.

What is the length of the wood that is needed to replace AD?

4.2 inches

5.7 inches

2.5 inches

1.3 inches

Question 16

(04.02 MC)

Leo drew a line that is perpendicular to the line shown on the grid and passes through point (F, G). Which of the following is the equation of Leo's line?

line on coordinate plane passing through 0 comma 3 and 1 comma 1

y G = 2(x F)

y + F = 2(x + G)

y + F = one half(x + G)

y G = one half(x F)

Question 17

(04.03 MC)

Calculate the area of triangle ABC with altitude BD, given A (6, 0), B (0, 0), C (0, 6), and D (3, 3).

18 square units

9 square units

18.5 square units

21 square units

Question 18

(04.01 LC)

Segment AB has point A located at (8, 9). If the distance from A to B is 10 units, which of the following could be used to calculate the coordinates for point B

10 = square root of the quantity of x plus 8 all squared plus y plus 9 all squared

10 = square root of the quantity of x plus 9 all squared plus y plus 8 all squared

10 = square root of the quantity of x minus 8 all squared plus y minus 9 all squared

10 = square root of the quantity of x minus 9 all squared plus y minus 8 all squared