Two sides of a triangle are \(50\) m and \(60\) m long. The angle included between these sides is \(30^\circ\). What is the interior angle opposite the longest side?
A\(93.74^\circ\)
B\(92.74^\circ\)
C\(90.74^\circ\)
D\(86.38^\circ\)
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Mathematics · Question Bank
Analytic Geometry
178 questions · page 2 of 9
A circle with radius \(6\) cm has half its area removed by cutting off a border of uniform width. Find the width of the border.
A1.76 cm
B1.35 cm
C1.98 cm
D2.03 cm
The area of a circle is \(89.42\) sq. inches. What is its circumference?
A32.25 in.
B33.52 in.
C35.33 in.
D35.55 in.
A square section ABCD has one of its sides equal to x. Point E is inside the square forming an equilateral triangle BEC having one side equal in length to the side of the square. Find the angle AED.
A\(130^\circ\)
B\(140^\circ\)
C\(150^\circ\)
D\(160^\circ\)
The area of a circle circumscribing about an equilateral triangle is \(254.47\) sq. m. What is the area of the triangle in sq. m?
A100.25
B102.25
C104.25
D105.25
What is the area in sq. cm of the circle circumscribed about an equilateral triangle with a side \(10\) cm long?
A104.7
B105.7
C106.7
D107.7
The area of a triangle inscribed in a circle is \(39.19 \text{ cm}^2\) and the radius of the circumscribed circle is \(7.14\) cm. If the two sides of the inscribed triangle are \(8\) cm and \(10\) cm, respectively, find the third side.
A11 cm
B12 cm
C13 cm
D14 cm
The area of a triangle is \(8346\) sq. m and two of its interior angles are \(37^\circ 25'\) and \(56^\circ 17'\). What is the length of the longest side?
A171.5 m
B181.5 m
C191.5 m
D200.5 m
The angle of a sector is \(30^\circ\) and the radius is \(15\) cm. What is the area of the sector in cm\(^2\)?
A59.8
B89.5
C58.9
D85.9
Two perpendicular chords both \(5\) cm from the center of a circle divide the circle into four parts. If the radius of the circle is \(13\) cm, find the area of the smallest part.
A\(30 \text{ cm}^2\)
B\(31 \text{ cm}^2\)
C\(32 \text{ cm}^2\)
D\(33 \text{ cm}^2\)
The distance between the centers of the three circles which are mutually tangent to each other externally are \(10\), \(12\) and \(14\) units. The area of the largest circle is
A\(72 \pi\)
B\(23 \pi\)
C\(64 \pi\)
D\(16 \pi\)
The arc of a sector is \(9\) units and its radius is \(3\) units. What is the area of the sector in square units?
A12.5
B13.5
C14.5
D15.5
A circle having an area of \(452\) sq. m is cut into two segments by a chord which is \(6\) m from the center of the circle. Compute the area of the bigger segment.
A354.89 sq. m
B363.68 sq. m
C378.42 sq. m
D383.64 sq. m
A swimming pool is constructed in the shape of two partially overlapping identical circles. Each of the circles has a radius of \(9\) m and each circle passes through the center of the other. Find the area of the swimming pool.
A\(380 \text{ m}^2\)
B\(390 \text{ m}^2\)
C\(400 \text{ m}^2\)
D\(410 \text{ m}^2\)
Find the difference of the area of the square inscribed in a semi-circle having a radius of \(15\) m. The base of the square lies on the diameter of the semi-circle.
A\(171.5 \text{ cm}^2\)
B\(172.5 \text{ cm}^2\)
C\(173.5 \text{ cm}^2\)
D\(174.5 \text{ cm}^2\)
A rectangle ABCD which measures \(18\) cm. by \(24\) cm. is folded once, perpendicular to diagonal AC, so that the opposite vertices A and C coincide. Find the length of the fold.
A20.5 cm
B21.5 cm
C22.5 cm
D23.5 cm
A trapezoid has an area of \(36 \text{ m}^2\) and an altitude of \(2\) m. Its two bases have ratio of 4:5. What are the lengths of the bases?
A12, 15
B7, 11
C8, 10
D16, 20
A rhombus has diagonals of \(32\) and \(20\) inches. Determine its area.
A\(360 \text{ in}^2\)
B\(280 \text{ in}^2\)
C\(320 \text{ in}^2\)
D\(400 \text{ in}^2\)
If the sides of a parallelogram and an included angle are \(6\), \(10\) and \(100^\circ\) respectively, find the length of the shorter diagonal.
A10.63
B10.37
C10.73
D10.23
Find the area of a quadrilateral having sides \(AB = 10\) cm, \(BC = 5\) cm. \(CD = 14.14\) cm and \(DA = 15\) cm, if the sum of the opposite angles is equal to \(225^\circ\).
A96 sq. cm
B100 sq. cm
C94 sq. cm
D98 sq. cm