Deck 12: Introduction to Trigonometry

Question 1

Find the exact value of sec 30°.

Answer 1

NOT ANSWERED.

Question 2

As increases from 0 ° to 90 ° , sin increases also.

Answer 2

False

Question 3

In right triangle RST , m = 90 ° . If RS = 13 and ST = 17, find m to the nearest degree.

Answer 3

NOT ANSWERED.

Question 4

As increases in size from 0 ° to 90 ° , the value of cos also increases.

Question 5

The lengths of the sides of a right triangle are a , b , and c (the hypotenuse). Given that , find an expression for .

Question 6

In , AB = 6 cm, AD = 10 cm, and m = 65 ° . To the nearest tenth of centimeter,
find the length of altitude from B to side .

Question 7

For a right triangle in which , it follows that .

Question 8

Find the exact value of sin 30°.

A)
B)
C)
D)

Question 9

Using a calculator, the value of sin 54° is approximately 0.8090.

Question 10

For right triangle ABC , m = 90 ° . If b = 8 and c = 12, find cos B (or cos ).

Question 11

In a right triangle, the cosine ratio takes the form .

Question 12

In a right triangle with acute angle measures of and , sin . It follows that:

A)
B) 53 °
C)
D)

Question 13

In a triangle, the angle measures are , , and and opposite sides have lengths a , b , and c respectively. Based upon the Law of Cosines, what expression is equivalent to ?

Question 14

If m = 90 ° and m = 35 ° , one would use sin A to find the value of b .

Question 15

In the figure, is a right angle. Find the value of sin A (also known as sin ).

A)
B)
C)
D)

Question 16

In the triangle shown, c = 12, m = 90 ° , and m = 63 ° . To the nearest tenth of a unit, find the length b .

Question 17

In , is a right angle. If a = 5 and c = 13, find sin B (also known as sin )

A)
B)
C)
D)None of These

Question 18

Without using a calculator, which number is larger . . . cos 56° or cos 63°?

Question 19

In , is a right angle while SR = 11 and ST = 13. To the nearest degree, what is the measure of ?

Question 20

The slant height of a regular square pyramid meets the apothem of the base to form an angle measuring 59°. If the length of the slant height is 12.6 cm, find the length of each side of the square base of the pyramid. Provide the answer correct to the nearest tenth of a centimeter.

Question 21

Given that cos = 0.5, it follows that

A)sin = 0.5
B)cot = 2
C)csc = 2
D) = 60 °

Question 22

In the figure, m = 90 ° and m = 27 ° . Find the length of b correct to nearest tenth of a unit.

A)9.8
B)10.7
C)10.9
D)11.2

Question 23

Find the exact value of cos 30°.

Question 24

From a distance of 345 feet across a flat meadow, the top of a tower is seen through an angle of elevation of 27°. To the nearest foot, how tall is the tower?

Question 25

In , m = 90 ° . If s = 4 and t = 5, find the exact value of cos S .

A) or
B) or
C)
D)None of These

Question 26

In the figure, m = 90 ° and m = 29 ° . If c = 17.4, find b to the nearest tenth of unit..

A)15.2
B)16.3
C)8.4
D)19.9

Question 27

In the right triangle shown, it follows that tan 45° = 1.

Question 28

To find the length of apothem a in a regular hexagon with sides of length 6 cm, one could solve the equation tan 60 ° = .

Question 29

In a right triangle, . Find the value of .

Question 30

Find the exact value of tan 60°.

Question 31

If m 90 ° in the triangle shown, then sin .

Question 32

If in the right triangle with acute angles and , it follows that .

Question 33

The sides of the square base of a regular pyramid measure 8 inches each while the altitude measures 10 inches. To the nearest degree, find the measure of the angle formed by the slant height and the apothem of square base of the pyramid shown.

A)56 °
B)60 °
C)64 °
D)68 °

Question 34

When = 90 ° , a form of the Law of Cosines reduces to Heron's Formula.

Question 35

In a right triangle, the tangent ratio of an angle has the form .

Question 36

In a right triangle, the legs have lengths of 5 ft and 12 ft. Using these measures, which ratio (sine, cosine, or tangent)would be used to find the measure of the acute angle that is formed by the hypotenuse and the leg of length 12 feet?

Question 37

In the triangle shown, m = 90 ° . Find an expression for cos B (also called cos ).

Question 38

In a right triangle, the measures of the angles are , , and = 90 ° . With the lengths of the opposite sides being a , b , and c respectively, find tan .

Question 39

In the 3-4-5 right triangle, find m to the nearest degree.

Question 40

The pitch (or slope)of a roof is . To the nearest degree, find the measure of the smaller acute angle shown in the drawing.

A)19 °
B)21 °
C)23 °
D)25 °

Question 41

In the isosceles triangle shown, the legs are 10 inches each while m = 40 ° . Find the length of base correct to the nearest tenth of an inch.

Question 42

In , m = 42 ° while b = 5.6 and c = 7.2. To the nearest tenth of a square unit, find the area of the triangle shown.

A)13.5
B)15.0
C)27.0
D)30.0

Question 43

In , s = 6, t = 9, and m = 38 ° . Find m to the nearest degree.

A)67 °
B)69 °
C)73 °
D)None of These

Question 44

If m = 67 ° , b = 17.4 cm, and c = 12.5 cm, find the area of correct to the nearest square centimeter.

Question 45

is not a right triangle. If m = 72 ° , m = 38 ° , AB = 12.4, and BC = 19.2, find the length of correct to the nearest whole unit.[Hint: Consider altitude .]

Question 46

On a rectangular wall WXYZ under construction, a diagonal serves as a brace. If YX = 8 ft and WX = 12.5 ft, find the measure of the angle formed by and .Provide answer to the nearest tenth of a degree.

Question 47

In , b = 6.0 inches, m = 40 ° and m = 65 ° . To the nearest tenth of an inch, find the length c .

A)7.8 in
B)8.5 in
C)8.9 in
D)None of These

Question 48

Find the exact value of the expression °   ° .

Question 49

For the isosceles triangle shown, the measure of the vertex angle is m = 38 ° .If AB = BC = 6.8, find AC to the nearest tenth of a unit.

A)4.4 units
B)4.6 units
C)5.4 units
D)6.0 units

Question 50

In the right triangle shown, m = 90 ° . What is the value of the expression ( )?

Question 51

In , AB = 12, AD = 18, and m = 56 ° . To the nearest square unit, find the area of .

Question 52

In , the lengths of the sides are a = 8, b = 10, and c = 12. To the nearest degree, find m .

A)75 °
B)79 °
C)83 °
D)87 °

Question 53

In any right triangle for which is the measure of an acute angle, it follows that .

Question 54

If m = 90 ° while m and m in , an expression representing the sum ( )is .

Question 55

For any angle measure (where ° and ° ), find the value of the expression .

A)1
B)2
C)3
D)None of These

Question 56

In the isosceles triangle shown, m = 30 ° while AC = AB = 10 inches. Find the area of the triangle.

Question 57

For an acute triangle, suppose that you know the measures of each angle , , and as well as the lengths a and c for two sides. State the formula that you would use to find the area A of the triangle.

Question 58

In , m = 39 ° while s = 6 and t = 9. Find m to the nearest degree.

Question 59

Across the flat terrain, Meg and Mara see a forest ranger tower that they know is 120 feet high. If their angle of elevation to the top of the tower is 3 degrees, how far (to the nearest foot)will Meg and Mara have to walk to get to the tower? [Hint: 1 mile = 5280 feet.]

A)2,290 ft
B)2,293 ft
C)2,500 ft
D)None of These

Question 60

The exact value for both sin 45 ° and cos 45 ° is .

Question 61

Correct to tenths, find the value of the expression 34 ° + 34 ° .

A)1.0
B)1.2
C)0.8
D)None of These

Question 62

In a triangle with angle measures A , B , and C , the Law of Sines can be written .

Question 63

The lengths of sides for a regular pentagon are 6 inches each. To the nearest tenth of an inch, find the length of the radius of the pentagon.

A)4.1 in
B)4.7 in
C)4.9 in
D)5.1 in

Question 64

If the sides of have measures a = 3, b = 4, and c = 5, then the measure of (the angle opposite the side of length c )is 90 ° .

Question 65

In (not shown), m = 90 ° . If a = 8, b = 15, and c = 17, find m correct to the nearest degree.

A)28 °
B)52 °
C)62 °
D)67 °

Question 66

For the triangle with angle measures , , and for angles A , B , and C respectively, the area of the triangle can be calculated by using the formula .