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Geometry and Trigonometry
Questions
What is the value of tan 92 π / 3 ?
Q1
A ) - √3
B ) - √3 / 3
C ) √3 / 3
D ) -√3
Q2
The graph of x² + x + y² + y = 199/2 in the xy-plane is a circle. What is the length of the circle’s radius?
Q3
In convex pentagon A B C D E, segment AB is parallel to segment DE . The measure of angle B is 139 degrees, and the measure of angle D is 174 degrees. What is the measure, in degrees, of angle C ?
Q4
The side lengths of right triangle R S T are given. Triangle R S T is similar to triangle is similar to triangle U V W , where S corresponds to V and T corresponds to W . What is the value to tanW ?
R S = 20
S T = 48
T R = 52
A ) 5 / 13
B ) 5 / 12
C ) 12 / 13
D ) 12 / 5
Q5
In the triangle shown, R S = √105 . What is the value of Sin R ?
Q6
Quadrilateral P' Q' R' S' is similar to quadrilateral P Q R S where P , Q , R and S correspond to P' , Q' , R' and S' respectively. The measure of angle P is 30 degree , the measure of angle Q is 50 degree , and the measure of angle R is 70 degree The length of each side of P', Q' , R' and S ' is 3 times the length of each corresponding side of P Q R S. What is the measure of angle P' ?
A ) 10 degree
B ) 30 degree
C ) 40 degree
D ) 90 degree
Q7
In â–³A B C, ∠B is a right angle and the length of BC is 136mm. If cos A = 3 / 5. what is the length, in millimeters, of AB ?
A ) 34
B ) 102
C ) 136
D ) 170
Q8
The measure of angle Z is 60 degree . What is the measure, in radians, of angle Z ?
A ) (1/ 6) Π
B ) (1/ 3) Π
C ) (2/ 3) Π
D) 1 Π
Q9
Rectangles A B C D and Q R S T shown are similar, where A , B , C and D correspond to Q , R , S and T respectively. What is the length, in inches (in) of A D ?
A ) 60
B ) 24
C ) 17
D ) 10
Q10
A cylinder has a diameter of 8 inches and a height of 12 inches. What is the volume, in cubic inches, of the cylinder?
A ) 16 Π
B ) 96 Π
C ) 192 Π
D ) 768 Π
Q11
For the triangle shown, which expression represents the value of a ?
Q12
In triangle ABC, the measure of angle A is 54°, the measure of angle B is 90°, and the measure of angle C is (k/2). What is the value of k?
A ) 36
C ) 72
Q13
In the figure shown, lines r and s are parallel, and line m intersects both lines. If y < 65 which of the following must be true?
A.) X < 115
B ) 45
D ) 108
B.) x > 115
Q14
Q15
C.) x + y < 180
The circle shown has center O, circumference 144π, and diameters PR and QS. The length of arc PS is twice the length of arc PQ. What is the length of arc QR?
A ) 24 Π
C ) 72 Π
In the figure shown, triangle CAE is similar to triangle CBD. The measure of angle CBD is 57 degree , and AE = 26(BD) What is the measure of angle CAE ?
D.) x + y > 180
B ) 4 8Π
D ) 96 Π
Q16
What is the area, in square centimeters, of a rectangle with a length of 34 centimeters (cm) and a width of 29 cm?
Q17
Triangle R has an area of 80 square centimeters (cm²). Square S has side lengths of 4 cm. What is the total area of triangle R and square S, in cm²?
A ) 44
B ) 42
C ) 84
D ) 96
Q18
In the figure shown, triangle JKL is similar to triangle RST, where J corresponds to R and K corresponds to S. The length of overline JK is 15, and the perimeter of triangle JKL is 36. The length of overline RS is 135. What is the perimeter of triangle RST?
A ) 324
B ) 540
C ) 2,916
D ) 8,100
Q19
Which equation shows the relationship between the side lengths of the given triangle?
Q20
The area of a rectangle is 57 square inches. The length of the longest side of the rectangle is 19 inches. What is the length, in inches, of the shortest side of this rectangle?
stay tuned - more questions & solution will be added soon !
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