Question 1

Find the exact value of sec 30°.

Accepted Answer

NOT ANSWERED.

Question 2

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

Accepted Answer

False

Question 3

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

Accepted Answer

NOT ANSWERED.

Question 4

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

Accepted Answer

The answer of As  increases in size from 0...

Question 5

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

Accepted Answer

The answer of The lengths of the sides of a...

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  .

Accepted Answer

The answer of In  , AB = 6 cm,...

Question 7

For a right triangle in which  , it follows that  .

Accepted Answer

The answer of For a right triangle in which ...

Question 8

Find the exact value of sin 30°.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the exact value of sin 30°.
A)...

Question 9

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

Accepted Answer

This is correct. When using a calculator in degree mode, sin 54° is approximately equal to 0.8090.

Question 10

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

Accepted Answer

The answer of For right triangle ABC , m ...

Question 11

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

Accepted Answer

The cosine ratio in a right triangle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. Therefore, it cannot take the form of a hexadecimal number (e.g. 11ebfb55_24ca_1fca_9d86_31a6453b2b73).

Question 12

In a right triangle with acute angle measures of  and  , sin  . It follows that:
A) 
B)  53 °
C) 
D)

Accepted Answer

The answer of In a right triangle with acute angle...

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  ?

Accepted Answer

The answer of In a triangle, the angle measures are...

Question 14

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

Accepted Answer

If we draw a right triangle with angle A = 90° and angle B = 35°, then angle C = 55° (since the angles of a triangle add up to 180°). Let b be the length of the side opposite angle B. Then, we can use the sine function to find b:

sin B = opposite/hypotenuse
sin 35° = b/hypotenuse

We can solve for hypotenuse:

hypotenuse = b/sin 35°

Now, we need to find the length of the side adjacent to angle B, which we can call a. We can use the angle sum property of triangles to find angle A:

angle A = 180° - angle B - angle C
angle A = 180° - 35° - 55°
angle A = 90°

Since angle A is a right angle, the side opposite it (which we have been calling hypotenuse) is actually the hypotenuse of the triangle. Therefore, we can use the sine function again to relate the length of side a to the hypotenuse:

sin A = opposite/hypotenuse
sin 90° = a/hypotenuse
1 = a/hypotenuse

So, we have:

a = hypotenuse = b/sin 35°

Therefore, we can use sin A (which equals 1) to find b:

b/sin 35° = hypotenuse = a = b/1

Simplifying, we get:

b/sin 35° = b/1

Multiplying both sides by sin 35°, we get:

b = sin 35° * b/ sin 35°

Simplifying, we get:

b = 1 * b

Therefore, we have:

b = b

This is true for any value of b, so we don't need to know the specific value of angle A (which happens to be 90° in this case) in order to 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)

Accepted Answer

The answer of In the figure,  is a right...

Question 16

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

Accepted Answer

The answer of In the triangle shown, c = 12,...

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

Accepted Answer

The answer of In  ,  is a right...

Question 18

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

Accepted Answer

The answer of Without using a calculator, which number is...

Question 19

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

Accepted Answer

The answer of In  ,  is a right...

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.

Accepted Answer

The answer of The slant height of a regular square...

Quiz 12: Introduction to Trigonometry

Find the exact value of sec 30°.

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

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

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

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

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 .

For a right triangle in which , it follows that .

Find the exact value of sin 30°.

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

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

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

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

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 ?

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

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

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

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

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

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

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.