Regents Exam Questions by Topic Page 1 TRIANGLES: Using ...

Regents Exam Questions by Topic Page 1TRIANGLES: Using Trigonometry to Find Areawww.jmap.orgNAME:_____________________________1. 060704b, P.I. A2.A.74Jack is planting a triangular rose garden. Thelengths of two sides of the plot are 8 feet and12 feet, and the angle between them is 87°.Which expression could be used to find thearea of this garden?[A] 8• 12• sin 87°[B] 1 8 12 872 • • • sin °3. 080226b, P.I. A2.A.74Two sides of a triangular-shaped poolmeasure 16 feet and 21 feet, and the includedangle measures 58°. What is the area, to thenearest tenth of a square foot, of a nyloncover that would exactly cover the surface ofthe pool?[C] 1 2• 8 • 12 • cos 87 °[D] 8• 12• cos87°2. 010225b, P.I. A2.A.74The accompanying diagram shows the floorplan for a kitchen. The owners plan to carpetall of the kitchen except the "work space,"which is represented by scalene triangle ABC.Find the area of this work space to the nearesttenth of a square foot.4. 080324b, P.I. A2.A.74The triangular top of a table has two sides of14 inches and 16 inches, and the anglebetween the sides is 30°. Find the area of thetabletop, in square inches.5. 060525b, P.I. A2.A.74A landscape architect is designing a triangulargarden to fit in the corner of a lot. The cornerof the lot forms an angle of 70°, and the sidesof the garden including this angle are to be 11feet and 13 feet, respectively. Find, to thenearest integer, the number of square feet inthe area of the garden.6. 010723bIn ΔABC, AC = 18, BC = 10, andcos C = 1 .2Find the area of ΔABC to thenearest tenth of a square unit.

Regents Exam Questions by Topic Page 2TRIANGLES: Using Trigonometry to Find Areawww.jmap.orgNAME:_____________________________7. 080628bThe accompanying diagram shows atriangular plot of land that is part of Fran'sgarden. She needs to change the dimensionsof this part of the garden, but she wants thearea to stay the same. She increases thelength of side AC to 22.5 feet. If angle Aremains the same, by how many feet shouldside AB be decreased to make the area of thenew triangular plot of land the same as thecurrent one?9. 060121bGregory wants to build a garden in the shapeof an isosceles triangle with one of thecongruent sides equal to 12 yards. If the areaof his garden will be 55 square yards, find, tothe nearest tenth of a degree, the three anglesof the triangle.10. 010924bIn the accompanying diagram ofparallelogram ABCD, m∠ A = 30, AB = 10,and AD = 6. What is the area ofparallelogram ABCD?8. 060825bThe accompanying diagram shows the peakof a roof that is in the shape of an isoscelestriangle. A base angle of the triangle is 50°and each side of the roof is 20.4 feet.Determine, to the nearest tenth of a squarefoot, the area of this triangular region.

Regents Exam Questions by Topic Page 1TRIANGLES: Using Trigonometry to Find Areawww.jmap.org[1] B[2][3][2] 164.2, and appropriate work is shown.[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] 164.2, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.[2] 142.5, and appropriate work is shown,such as 1 ( 16)( 21)(sin 58 ).2 °[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] An incorrect trigonometric function isused, but an appropriate answer is found, suchas 1 ( 16)( 21)(sin 58° ), resulting in an answer2of 89 or 89.0.or [1] 142.5, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.[2] 56, and appropriate work is shown, suchas 1 14 16 302 ⋅ ⋅ ⋅sin .[5][6][2] 67, and appropriate work is shown, such1as A = ( 11)( 13)sin 70°.2[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 67, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.[2] 77.9, and appropriate work is shown, suchas evaluating 1 2 ab sin C.[1] Appropriate work is shown, but onecomputational or rounding error is made.or [1] Appropriate work is shown, but oneconceptual error is made, such as writingcos C.or [1] 77.9, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.[4][1] Appropriate work is shown, but onecomputational error is made.or [1] Appropriate work is shown, but oneconceptual error is made.or [1] 56, but no work is shown.[0] A zero response is completely incorrect,irrelevant, or incoherent or is a correctresponse that was obtained by an obviouslyincorrect procedure.