Question 1

Give the complement and the supplement of angle  z .  ​
A)Complement: 90° -  z  Supplement: 90° +  z
B)Complement: 180° -  z  Supplement: 90° -  z
C)Complement: 90° -  z  Supplement: 180° -  z
D)Complement: - z  Supplement: 180° -  z
E)Complement: 90° +  z  Supplement: 90° -  z

Accepted Answer

The complement of an angle is what, when added to it, equals 90 degrees. The supplement of an angle is what, when added to it, equals 180 degrees. Therefore, the complement is 90° - z and the supplement is 180° - z.

Question 2

Indicate if the angle 50° is acute or obtuse. Then give the complement and the supplement of the angle. ​
A)obtuse; complement: 040° supplement: 130°
B)acute; complement: 040 ° supplement: 130 °
C)acute; complement: 040° supplement: -50°
D)obtuse; complement: 040° supplement: -50°
E)acute; complement: 130° supplement: 040°

Accepted Answer

The angle 50° is acute. The complement of an acute angle is always obtuse and its supplement is always greater than 90° and obtuse. Therefore, the correct answer is B, where the complement is 40° and the supplement is 130°.

Question 3

The figure shows a walkway with a handrail. Angle α  is the angle between the walkway and the horizontal, while angle  β  is the angle between the vertical posts of the handrail and the walkway. Assume that the vertical posts are perpendicular to the horizontal.  Find α  if β = 52°.
A)α = 57°
B)α  = 123 °
C)α  = 38 °
D)α  = 128 °
E)α  = 52 °

Accepted Answer

First, we notice that α and β are alternate interior angles formed by a transversal (the posts of the handrail) crossing two parallel lines (the walkway and the ground). Therefore, α = β.

Given that β = 52°, we have α = 52° as well.

Therefore, the answer is C, α = 38°.

Question 4

An escalator in a department store is to carry people a vertical distance of 25 feet between floors. How long is the escalator if it makes an angle of 30° with the ground? ​
A)42 feet
B)31 feet
C)41 feet
D)50 feet
E)39 feet

Accepted Answer

The answer of An escalator in a department store is...

Question 5

Find the remaining sides of a 30° - 60° - 90° triangle if the side opposite 60° is 18.
A)  ,  
B)  ,  
C)​  ,  
D)  ,  
E)  ,

Accepted Answer

In a 30°-60°-90° triangle, the side opposite the 30° angle is half the length of the hypotenuse (which is the side opposite the 90° angle), and the side opposite the 60° angle is √3 times the length of the side opposite the 30° angle.

Therefore, in this triangle, the hypotenuse is 2(18) = 36, and the side opposite the 30° angle is 18/2 = 9.

The side opposite the 60° angle is √3 times the side opposite the 30° angle, so it is √3(9) = 9√3.

Thus, the remaining sides of the triangle are 9 and 9√3.

Therefore, the answer is B, (11ebf5ef_bb55_e7bd_95d1_8d6985153750_TBX9354_11,11ebf5ef_bb55_e7be_95d1_93e965c0128b_TBX9354_11).

Question 6

Find β  if B = 4 β .  Remember: The sum of the three angles in any triangle is always 180°.
A)β = 72°
B)β  = 19 °
C)β  = 21 °
D)β  = 18 °
E)β  = 69 °

Accepted Answer

The answer of Find β  if B = 4 β...

Question 7

Suppose ABC  is a right triangle with C = 90°. If a = 6 and c = 10, find b . ​
A)b = 9
B)b  = 13
C)b  = 8
D)b  = 4
E)b  = 10

Accepted Answer

In a right triangle, the Pythagorean theorem states that $a^2 + b^2 = c^2$. Given $a = 6$ and $c = 10$, we can solve for $b$: $6^2 + b^2 = 10^2$, which simplifies to $36 + b^2 = 100$. Subtracting 36 from both sides gives $b^2 = 64$, and taking the square root of both sides gives $b = 8$.

Question 8

Solve for x .   , b = 1 ​
A)x = 1
B)x  = 7
C)x  = 3
D)x  = 5
E)x  = 4

Accepted Answer

The answer of Solve for x .   ,...

Question 9

The object shown in the figure is a cube (all edges are equal in length).  Suppose the length of diagonal CF  in the figure is  feet. What is the length of edge  AC ? ​
A)5 inches
B)   inches
C)   inches
D)   inches
E)   inches

Accepted Answer

The answer of The object shown in the figure is...

Question 10

An isosceles triangle is a triangle in which two sides are equal in length. The angle between the two equal sides is called the vertex angle, while the other two angles are called the base angles. If the vertex angle is 60°, what is the measure of the base angles?
A)50°
B)60°
C)45°
D)80°
E)65°

Accepted Answer

In an isosceles triangle, the two base angles are equal, and the sum of all angles in any triangle is 180°. Given the vertex angle is 60°, the sum of the two base angles is 180° - 60° = 120°. Since the base angles are equal, each is 120° / 2 = 60°.

Question 11

Find the remaining side of a 45° - 45° - 90° triangle if the shorter sides are each  ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

In a 45°-45°-90° triangle, the hypotenuse is equal to the length of the shorter sides multiplied by the square root of 2. Therefore, the remaining side is 11 x √2 which is approximately equal to 15.56. The closest answer choice to 15.56 is A, 11ebf5ef_bb55_4b60_95d1_cb16b866f0fc_TBX9354_11.

Question 12

Suppose ABC  is a right triangle with C = 90°. If a = 6 and b = 8, find c .
A)c = 9
B)c  = 18
C)c  = 10
D)c  = 15
E)c  = 6

Accepted Answer

Using the Pythagorean Theorem, we have:
c^2 = a^2 + b^2
c^2 = 6^2 + 8^2
c^2 = 36 + 64
c^2 = 100
c = sqrt(100)
c = 10. Therefore, the answer is choice C.

Question 13

Find r  if AB = 32 and AD = 40.  ​
A)r = 14
B)r  = 10
C)r  = 9
D)r  = 7
E)r  = 5

Accepted Answer

The answer of Find r  if AB = 32 and AD = 40....

Question 14

Find the remaining sides of a 30° - 60° - 90° triangle if the longest side is 10. ​
A)  ,  
B)4,  
C)3,  
D)5,  
E)  ,

Accepted Answer

The answer of Find the remaining sides of a 30°...

Question 15

The object shown in the figure is a cube (all edges are equal in length).  If the length of each edge of the cube shown in the figure is 1 inch0, find the length of diagonal CE . ​
A)   inches
B)   inch0
C)   inches
D)   inches
E)   inches

Accepted Answer

The answer of The object shown in the figure is...

Question 16

Find A  if B = 20° and  α +  β = 120°.  Remember: The sum of the three angles in any triangle is always 180°.
A)A = 60°
B)A  = 50 °
C)A  = 70 °
D)A  = 100 °
E)A  = 40 °

Accepted Answer

The answer of Find A  if B = 20° and  α + ...

Question 17

Find the remaining sides of a 45° - 45° - 90° triangle if the longest side is 4.
A)  ,  
B)  ,  
C)  ,  
D)​  ,  
E)  ,

Accepted Answer

The answer of Find the remaining sides of a 45° -...

Question 18

Solve for x .  a = 5,   ​
A)x = 9
B)x  = 4
C)x  = 6
D)x  = 5
E)x  = 7

Accepted Answer

We notice that the first term is 5 and the second term is 11, which differ by 6. The third term is therefore 17, and the fourth term is 23. Continuing this pattern, we find that the nth term is 6n - 1. So, the value of x in the second term is 5 + 3(11 - 5) = 5 + 18 = 23, and the value of x in the third term is 5 + 4(11 - 5) = 5 + 24 = 29. Therefore, we have:
6x - 1 = 23
6x = 24
x = 4
And,
6x - 1 = 29
6x = 30
x = 5
Since x can only have one value, the answer is D.

Question 19

A searchlight rotates through one complete revolution every 6 seconds. How long does it take the light to rotate through 300°? ​
A)4 sec.
B)7 sec.
C)2 sec.
D)3 sec.
E)5 sec.

Accepted Answer

The answer of A searchlight rotates through one complete revolution...

Question 20

Find AB  if BC = 3, BD = 5, and AD = 6.  ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find AB  if BC = 3, BD = 5,...

Quiz 1: The Six Trigonometric Functions

Give the complement and the supplement of angle z .

Indicate if the angle 50° is acute or obtuse. Then give the complement and the supplement of the angle.

The figure shows a walkway with a handrail. Angle α is the angle between the walkway and the horizontal, while angle β is the angle between the vertical posts of the handrail and the walkway. Assume that the vertical posts are perpendicular to the horizontal. Find α if β = 52°.

An escalator in a department store is to carry people a vertical distance of 25 feet between floors. How long is the escalator if it makes an angle of 30° with the ground?

Find the remaining sides of a 30° - 60° - 90° triangle if the side opposite 60° is 18.

Find β if B = 4 β . Remember: The sum of the three angles in any triangle is always 180°.

Suppose ABC is a right triangle with C = 90°. If a = 6 and c = 10, find b .

Solve for x . , b = 1

The object shown in the figure is a cube (all edges are equal in length) . Suppose the length of diagonal CF in the figure is feet. What is the length of edge AC ?

An isosceles triangle is a triangle in which two sides are equal in length. The angle between the two equal sides is called the vertex angle, while the other two angles are called the base angles. If the vertex angle is 60°, what is the measure of the base angles?

Find the remaining side of a 45° - 45° - 90° triangle if the shorter sides are each

Suppose ABC is a right triangle with C = 90°. If a = 6 and b = 8, find c .

Find r if AB = 32 and AD = 40.

Find the remaining sides of a 30° - 60° - 90° triangle if the longest side is 10.

The object shown in the figure is a cube (all edges are equal in length) . If the length of each edge of the cube shown in the figure is 1 inch0, find the length of diagonal CE .

Find A if B = 20° and α + β = 120°. Remember: The sum of the three angles in any triangle is always 180°.

Find the remaining sides of a 45° - 45° - 90° triangle if the longest side is 4.

Solve for x . a = 5,

A searchlight rotates through one complete revolution every 6 seconds. How long does it take the light to rotate through 300°?

Find AB if BC = 3, BD = 5, and AD = 6.

Quiz 1: The Six Trigonometric Functions

Give the complement and the supplement of angle z . ​

Indicate if the angle 50° is acute or obtuse. Then give the complement and the supplement of the angle. ​

The figure shows a walkway with a handrail. Angle α is the angle between the walkway and the horizontal, while angle β is the angle between the vertical posts of the handrail and the walkway. Assume that the vertical posts are perpendicular to the horizontal. Find α if β = 52°.

An escalator in a department store is to carry people a vertical distance of 25 feet between floors. How long is the escalator if it makes an angle of 30° with the ground? ​

Find the remaining sides of a 30° - 60° - 90° triangle if the side opposite 60° is 18.

Find β if B = 4 β . Remember: The sum of the three angles in any triangle is always 180°.

Suppose ABC is a right triangle with C = 90°. If a = 6 and c = 10, find b . ​

Solve for x . , b = 1 ​

The object shown in the figure is a cube (all edges are equal in length) . Suppose the length of diagonal CF in the figure is feet. What is the length of edge AC ? ​