Questions

1) Solve for “k”.

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2) Solve for “w”.

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3) Solve for “m”.

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4) True or False. Use cross multiplication to determine if the given ratios are equal.

True

False

5) Solve for “p”. Show a proportion for the solution, and then state the answer.

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6) Jaedyn conducted a popular opinion poll and found that 4 out of 7 people own a pet. There are about 1500 people living in Jaedyn’s town. Predict about how many people may own a pet in Jaedyn’s hometown. Show a proportion for the solution, and then state the answer. (Image: Ashley Cox / FreeDigitalPhotos.net)

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7) If a scale is “1 inch = 50 miles”, then the “real” length is __________ than the scaled length.

a.) shorter

b.) longer

8) If a scale is “1 inch = 0.001 in”, then the “real” length is __________ than the scaled length.

a.) shorter

b.) longer

9) What is the width (S) of the house? (1 space / 3.125 = ? spaces / S)

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10) What is the actual length (B) of the house including the garage?

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11) Refer to the scale on the map and use a ruler to determine how many inches represent 50 miles. What is the scale for the map?

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12) What is the (a) map distance and what is the (b) actual distance from Steubenville to Zanesville traveling along route 22?

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13) Select the BEST answer to complete the following statement: If two polygons are similar, then ...

a.) the corresponding angles and the corresponding sides are congruent.

b.) neither the corresponding angles nor the corresponding sides are congruent.

c.) the corresponding angles are congruent and the corresponding sides are not proportional.

d.) the corresponding angles are congruent and the corresponding sides are proportional.

14) What name is given to the ratio of the lengths of any two corresponding sides of similar polygons?

a.) Similar figure

b.) Similar polygon

c.) Scale factor

d.) Congruent

15) Are the following parallelograms similar? If yes, what is the scale factor?

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16) Are the following triangles similar? If yes, what is the scale factor?

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17) What is the value of “x”? Choose the correct proportion and solve for “x”.

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18) What is the value of “x”?

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19) A trigonometric ratio is a ratio between the lengths of the sides of what kind of triangle?

a.) Obtuse

b.) Acute

c.) Right

d.) Scalene

e.) Equilateral

20) Each of the given ratios represents a trigonometric ratio? Select the answer that matches the ratios with the trig functions in the given order from left to right.

a.) sin(x), cos(x), tan (x)

b.) cos(x), tan(x), sin(x)

c.) tan(x), sin(x), cos(x)

d.) sin(x), tan(x), cos(x)

e.) tan(x), cos(x), sin(x)

f.) cos(x), sin(x), tan(x)

21) Which trigonometric function is true about the right triangle shown below?

a.) tan(K) = j/h

b.) sin(L) = i/j

c.) sin(K) = i/h

d.) cos(K) = h/i

e.) sin(K) = i/j

22) What is (a) the sin L, (b) the cos L, and (c) the tan L?

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23) What is (a) the sin V, (b) the cos V, and (c) the tan V? Express each answer as a decimal rounded to the nearest hundredth.

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24) What is (a) the sin Q, (b) the cos Q, and (c) the tan Q?

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25) What is (a) the sin R, (b) the cos R, and (c) the tan R?

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26) What is the sine of the given angle?

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27) What is the cosine of the given angle?

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28) What is the tangent of the given angle?

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29) An ANGLE OF ELEVATION is formed by a horizontal line and a line of sight above it. A pole light casts a shadow of 26 meters long when the angle of elevation of the Sun is 60 degrees. How tall is the pole light? (Hint: Use the tangent ratio to solve.)

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30) Chad is building a staircase in his new log cabin. The distance between the first floor of his home and the second floor of his home is 15 feet. He has enough building material to build a staircase that is 20 feet in length. At what angle will the staircase be when Chad has completed it? Express the angle rounded to the nearest whole number.

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31) Calculate the length of each side of triangle RST. Use the “distance formula” or the Pythagorean Theorem, if needed. (a) What is the length of TS? (b)What is the length of SR? (c) What is the length of TR?

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32) What is (a) the sin T and (b) the measure of angle T?

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33) What is (a) the cos R and (b) the measure of angle R?

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