ABO is a circular sector having a central angleof 30', with O as the center. If point M islocated midway between OB, determine.thearea of ABM If the radius of the circle is 4 cm.á) 2.19 cmb) 3.22 cm?c) 3.80 cm?d). 1.89 cm?A regular octagon is to be cut out from asquare "section having a side of 16 m,Determine side of the octagon.a) 7.22b) 5.86c) 3.44d) 6,63A, B, and C are three points on a horizontalplane, which lie in a circle with AB asdiameter. PA is a flagpole. The angle ofelevation of P from B and C are 20° and 30',respectively. If AB = 25 m, find the length of· BC.a). 17.65bj 22.31c) 18.76dj 19.41A trapezium ABCD has smaller side ABparallel to the bigger side CD. Side AD makesan angle of 45* from the side CD while sideBC makes an angle of 60* with side CD. IfAD = 1 cm, compute the value of the side BC.a) 0.816b) 0.678c) 0.789d). 0.890A right circular cone is divided into 3 portionsA, B, and C by planes parallel to the base. Theheight of each portion is h and the base radiusof the cone A isrunits. Cone A is at the vertexof the big cone. Determine the 'ratio of thevolume of A to that of B.-a) 1:8b) 1:9c) 1:7d) 1:10A hole 100 mm in diameter is to be punchedout from a right circular cone having adiameter of 160 mm. Height of cone is 240cm. Determine the-length of the hole punchedout.a) 95 mmb) 90 mmc). 105 mmd) 110 mm Triangle ABC has sides AB = 20 m, BC = 40m, and CA = 50 m. if point D`is on themidpoint of line BC, determine the locatiori ofpolnt E from the verfex A along line AB suchthat the line DE willi divide the lot having equalAn observer at point A observed the angle of.elevation of 27 to the top of the pole. If hemove horizontally a distance "S" towards B,nearer to the pole, the angle of elevation of thepole at B is double that of A. Find the height ofthe pole.a) S Sin 48'b) S Sin 272.areas.,a) 0b) 1.4c) 2.5d) 3.7c). S Sin 54.d) S Sin 451.Points A and B are 100 m. apart horizontallyand are of the same elevation as the foot of abuilding. The angles of elevation of the top ofthe building from A and B are 21" and 32respectively. How far is A fro the building?a), 259.28 mb) 235.56 m4.Towers A and B stand on a leyel ground. Fromthe top of the tower A which is 30 m. high theangle, of elevation of the top of tower B is 48".From the same point, the angle of depressionof the foot of tower B is 26°. What is the heightof tower B in meters?a) 94.3 m-b) 98.3 mc) 243.34 md) 274.36 mc) 85.3 md) 87.3 m5.QRST is a quadnilateral inscribed in a circle of. radius Y. The interior angle QTS = 75' andthe angle QST is.equal to 45". Find the angleAt 1:30pm a motorcyde travels from point Bnorthward for 30 min. then eastward for onehour, then shifted N.30°E. If the constantspeed is 60 kph, how far dírectly from B, in kmwill it be after 2 hrs?a) 91.09 kmb) 93.59 kmRSQ if arc ST is twice the arc RSa) 45b) 438.c) 52d)c) 112.51 kmd) 72.53 km7.An isosceles triangle ABC is inscribed in acircle with its center at 0. The angle BOC is228", find the value of angle ÄBO, if angle- BAC between the equal sides AB and AC isequal to 66".a) 29*b) 33The sum of two angles is 1600 mils and theirdifference is 40 grads. Find the value of thebigger angle in degrees.a) 63b) 38"c) 78d) 28"c) 27d) ¸ 23*10.11.A vertical pole stands on a horizontal ground..· A geodetic engineer positioned due east of thepole measures the elevation of the top of thepole as 53.33 grads. He moves dué south 30m. and measures the elevation of the top ofthe pole as 782.22 mils.: Determine the heightof the pole in meters.a) 48.6b) 39.4The angle of elevation of the top of tower Bfrom the top of the tower A is 24 and theangle of elevation of the top of the tower Afrom the base of tower B is 48". If the height offower B is 80 m, find the height of tower A:a) 33.26· b) 42.81c) 44.8d). 58.6) 57.11d) 67.2413.14.1One diagonal of a parallelogram is 80.5 m. Itmakes an angle of 18'24" and 35'12'respectively, with the sides. Find the length ofSolve for x# Arc tan (1- x) + Arctan (1+ x) = Arc tan

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ABO is a circular sector having a central angleof 30', with O as the center. If point M islocated midway between OB, determine.thearea of ABM If the radius of the circle is 4 cm.á) 2.19 cmb) 3.22 cm?c) 3.80 cm?d). 1.89 cm?A regular octagon is to be cut out from asquare &#34;section having a side of 16 m,Determine side of the octagon.a) 7.22b) 5.86c) 3.44d) 6,63A, B, and C are three points on a horizontalplane, which lie in a circle with AB asdiameter. PA is a flagpole. The angle ofelevation of P from B and C are 20° and 30',respectively. If AB = 25 m, find the length of· BC.a). 17.65bj 22.31c) 18.76dj 19.41A trapezium ABCD has smaller side ABparallel to the bigger side CD. Side AD makesan angle of 45* from the side CD while sideBC makes an angle of 60* with side CD. IfAD = 1 cm, compute the value of the side BC.a) 0.816b) 0.678c) 0.789d). 0.890A right circular cone is divided into 3 portionsA, B, and C by planes parallel to the base. Theheight of each portion is h and the base radiusof the cone A isrunits. Cone A is at the vertexof the big cone. Determine the 'ratio of thevolume of A to that of B.-a) 1:8b) 1:9c) 1:7d) 1:10A hole 100 mm in diameter is to be punchedout from a right circular cone having adiameter of 160 mm. Height of cone is 240cm. Determine the-length of the hole punchedout.a) 95 mmb) 90 mmc). 105 mmd) 110 mm Triangle ABC has sides AB = 20 m, BC = 40m, and CA = 50 m. if point D`is on themidpoint of line BC, determine the locatiori ofpolnt E from the verfex A along line AB suchthat the line DE willi divide the lot having equalAn observer at point A observed the angle of.elevation of 27 to the top of the pole. If hemove horizontally a distance &#34;S&#34; towards B,nearer to the pole, the angle of elevation of thepole at B is double that of A. Find the height ofthe pole.a) S Sin 48'b) S Sin 272.areas.,a) 0b) 1.4c) 2.5d) 3.7c). S Sin 54.d) S Sin 451.Points A and B are 100 m. apart horizontallyand are of the same elevation as the foot of abuilding. The angles of elevation of the top ofthe building from A and B are 21&#34; and 32respectively. How far is A fro the building?a), 259.28 mb) 235.56 m4.Towers A and B stand on a leyel ground. Fromthe top of the tower A which is 30 m. high theangle, of elevation of the top of tower B is 48&#34;.From the same point, the angle of depressionof the foot of tower B is 26°. What is the heightof tower B in meters?a) 94.3 m-b) 98.3 mc) 243.34 md) 274.36 mc) 85.3 md) 87.3 m5.QRST is a quadnilateral inscribed in a circle of. radius Y. The interior angle QTS = 75' andthe angle QST is.equal to 45&#34;. Find the angleAt 1:30pm a motorcyde travels from point Bnorthward for 30 min. then eastward for onehour, then shifted N.30°E. If the constantspeed is 60 kph, how far dírectly from B, in kmwill it be after 2 hrs?a) 91.09 kmb) 93.59 kmRSQ if arc ST is twice the arc RSa) 45b) 438.c) 52d)c) 112.51 kmd) 72.53 km7.An isosceles triangle ABC is inscribed in acircle with its center at 0. The angle BOC is228&#34;, find the value of angle ÄBO, if angle- BAC between the equal sides AB and AC isequal to 66&#34;.a) 29*b) 33The sum of two angles is 1600 mils and theirdifference is 40 grads. Find the value of thebigger angle in degrees.a) 63b) 38&#34;c) 78d) 28&#34;c) 27d) ¸ 23*10.11.A vertical pole stands on a horizontal ground..· A geodetic engineer positioned due east of thepole measures the elevation of the top of thepole as 53.33 grads. He moves dué south 30m. and measures the elevation of the top ofthe pole as 782.22 mils.: Determine the heightof the pole in meters.a) 48.6b) 39.4The angle of elevation of the top of tower Bfrom the top of the tower A is 24 and theangle of elevation of the top of the tower Afrom the base of tower B is 48&#34;. If the height offower B is 80 m, find the height of tower A:a) 33.26· b) 42.81c) 44.8d). 58.6) 57.11d) 67.2413.14.1One diagonal of a parallelogram is 80.5 m. Itmakes an angle of 18'24&#34; and 35'12'respectively, with the sides. Find the length ofSolve for x# Arc tan (1- x) + Arctan (1+ x) = Arc tan

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ABO is a circular sector having a central angle of 30', with O as the center. If point M is located midway between OB, delermine the area of ABM if the radius of the cirde is 4 cm. á) 2.19 cm b) 3.22 cm? c) 3.80 cm? d). 1.89 cm?