10th Grade Sine And Cosine Laws - Mixed (Nikoleta Simeonova)

10 Questions | Total Attempts: 96

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10th Grade Sine And Cosine Laws - Mixed (Nikoleta Simeonova)

For your "fill in the blanks" answers, please use the following pattern: _ cm, _ cm Example: 1 cm, 2 cm


Questions and Answers
  • 1. 
    Given a triangle ABC with sides 4 cm and 6 cm. The angles opposite them are in the ratio 1:2. Find the third side.
  • 2. 
    Given the inscribed quadrilateral ABCD, where AB=66cm, BC=77cm and AC=77cm. The angle bisectors of angles B and D intersect each other in point L, which lies on the diagonal AC. Find CD and AD.
  • 3. 
    Given a triangle ABC, such that a+c=11cm, c>a, β=60° and r= cm. Find a, b, c, .
    • A. 

      3 cm, cm, 7 cm, 4 cm

    • B. 

      3 cm, cm, 7 cm, cm

    • C. 

      3 cm, 8 cm, 5 cm, 4 cm

    • D. 

      3 cm, 8 cm, 7 cm, cm

  • 4. 
    Given the right angle triangle ABC. Points K and L lie on the hypotenuse AB, so that AK=KL=LB. Find cosβ, if CK=.CL.
    • A. 
    • B. 
    • C. 
    • D. 
  • 5. 
    Given a parallelogram ABCD (angle BAD is an acute angle). The orthogonal projection of AD over AC is 8 cm; the orthogonal projection of CD over AC is 16 cm; BD-=22 cm. Find the sides of ABCD.
  • 6. 
    Given a parallelogram ABCD, AB=13 cm, AD=16 cm, BN=9 cm (BN is the median in triangle ABD). Find the diagonals of ABCD.
  • 7. 
    A is exterior point for the circle k. AB is a tangent to k, ACD is a secant to k. AD-AB=24 cm. Find BC, if BD=56 cm and angle BAC is 60 degrees.
  • 8. 
    Given a triangle ABC with circumradius R. D lies on the short arc BC. The chords AD and BC intersect each other in point M, so that angle BMD is 120 degrees, BM:MC=2:3; AB=R. Find BC.
    • A. 
    • B. 
    • C. 
    • D. 
  • 9. 
    A circle k is inscribed in triangle ABC. The tangent point D divides AC into segments AD=6 cm, DC=4 cm. Find the sides AB and BC, if angle BAC is 60 degrees.
  • 10. 
    Given the rhombus ABCD. The side DC is seen from point M (the midpoint of AB) at angle 60 degrees. Find AC, if MD=4, MC=6.
    • A. 
    • B. 
    • C. 
    • D. 

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