Study Set Content:
The intersection of the medians of the triangle is called
A. midpoint
B. centerpoint
C. incenter
D. orthocenter
Centroid
In a triangle, the lengths of two larger sides are 10 cm and 9 cm respectively. If the angles of the triangle are in arithmetic progression, then the length of the third side is the
A. 5 cm
B. 5 ± (sqrt of 6) cm
C. 5 (sq rt of 6) cm
D. 5 ± (sq rt of 3) cm
B. 5 ± (sqrt of 6) cm
The line in which the midpoint, orthocenter cimcumcenter and the ninepoint center lie.
C. Euler's line
A. bisector
B. perpendicular bisector
D. median
C. Euler's line
What is the intersection of the angle bisectors of a triangle?
A. incenter
C. orthocenter
B. circumcenter
D. midpoint
A. incenter
Compute the area of a triangle with sides of 5, 7 and 10.
A. 16.248
B. 40.248
C. 16.248
D. 28.248
A. 16.248
If two triangles have congruent bases, then the ratio of their areas equals the ratio of
A. their perimeter
B. their sides
C. the lengths of their altitudes
D. none of the above
C. the lengths of their altitudes
Which is identically equal to (sec A + tan A)?
A. 1
sec A-tan A
B. csc A-1
C. 2
1 - tan A
D. csc A + 1
A. 1
sec A-tan A
In a right angled triangle, the hypotenuse is four times as long as the perpendicular to it from the opposite vertex, one of the acute angle is
A 15 deg
B. 30 deg
C. 22.5 deg
D.45 deg
A 15 deg
An engineer left a point (point A) walking at 6.5 kps in a direction E 20° N (that is bearing of 70°). A cyclist leaves the same point at the same time in a direction E 40° S (that is bearing 130°) traveling at a constant speed. Find the average speed of the cyclist if the engineer and the cyclist are 80 km apart
after 5 hours.
A. 18.23 kph
C. 24.34 kph
B. 13.45 kph
D. 21.45 kph
A. 18.23 kph
The vertical angle to the top of a flagpole from point A on the ground is observed to be 37°11'. The observer walks 17 m directly away from point A and the flagpole to point B and find the new angle to be 25°43'. What is the approximate height of the flagpole?
A. 22 m
B. 10 m
C.82 m
D. 300 m
A. 22 m
What is an equivalent expression for sin2x?
A. ½ sin x cos x
C. -2 sin x cos x
B. 2 sin x cos (½ x)
D. 2 sin x
sec x
D. 2 sin x
sec x
Solve the equation cos2A=1-cos2A.
A. 45 deg. 315 deg
C. 45 deg, 135 deg
B. 45 deg, 125 deg
D. 45 deg, 225 deg
A. 45 deg. 315 deg
The area of an isosceles triangle is 72 m². If the two equal sides makes an angle of 20 deg with the third side, calculate the length of the longest side.
A. 28.13 m
C. 35.4 m
B. 32.15 m
D. 23.4 m
A. 28.13 m
The triangle with minimum perimeter but maximum area inscribed in another triangle is known as
A. Pedal triangle
C. Primitive triangle
B. Euclid's triangle
D. None of the above
A. Pedal triangle
Given the sides of a triangle as 3 m and 5 m. The third side is
A. between 3 m and 8 m
B. from 3 m to 7 m
C. greater than 8 m
D. from 2 m to 8 m
B. from 3 m to 7 m
What is the value of 450 deg in radians?
A. 5pi/4
C. 13pi/4
B. 5pi/2
D. 9pi/3
B. 5pi/2
Given the triangle ABC in which A = 30°30', b = 100 m and c = 200 m. Find the length of the side a.
A 124.64 m
B. 130.50 m
C. 142.24 m
D. 103.00 m
A 124.64 m
An isosceles right triangle has a perimeter of 17.071. Compute the area of the triangle in square units.
A. 11.5
B. 10.5
C. 15.5
D. 12.5
D. 12.5
The area of an isosceles triangle is 36 m² with 30° as the included angle of the two adjacent equal sides. Compute the perimeter of the triangle.
A. 30.21
B. 33.12
C. 24.57
D. 35.67
A. 30.21
To determine the width of a river a surveyor measures a line AB 120 m long on one bank. To a point C on the other bank he determines the angle BAC = 48°36' and the angle ABC = 54°42'. Find the width of the river.
A. 55.7
B. 70.3
C. 75.5
D. 45.3
C. 75.5
