Trigonometry 1

The questions are based on the figure below: 

Diagram of right angle triangle with angles A,B,C indicated, sides a, b, c indicated and angles alpha and beta indicated

  1. The area of the triangle is given by ... 

    (A)   A = ½ (a+b)c 
    (B)   A = ½\; a · b 
    (C)   A = ½\; a · c 
    (D)   A = a^2 + b^2 - c^2 

     
  2. Which expression is wrong: 

    (A)   c^2 = a^2 + b^2 
    (B)   c^2 - a^2 = b^2  
    (C)   b^2 - c^2 = a^2 
    (D)   b^2 - a^2 + 2a^2 = c^2  

    Correct = C


     
  3. Which expression regarding the values of the angles is right: 

    (A)   \alpha + \beta < 90^\circ 
    (B)   \alpha + \beta > 90^\circ 
    (C)   180^\circ + (\alpha + \beta) = 360^\circ 
    (D)   180^\circ - \alpha = 90^\circ + \beta 

    Correct = D


     
  4. If the length of side c is 13\; \text {cm}, the length of side a is 5\; \text{cm}, what will be the length of side b? 

    (A)   7\; \text {cm} 
    (B)   8\; \text {cm} 
    (C)   12\; \text {cm} 
    (D)   18\; \text{cm} 

    Correct = C


     
  5. Which expression is correct? 

    (A)   \sin \beta = c/b 
    (B)   \sin \beta = b/a 
    (C)   \sin \alpha = b/c 
    (D)   \sin \alpha = a/c 

    Correct = D


     
  6. Spot the mistake: 

    (A)   \sin \beta = b/a 
    (B)   \sin \alpha = a/c 
    (C)   \cos \beta = a/c 
    (D)   \cos \alpha = b/c 

    Correct = A


     
  7. Identify the wrong expression: 

    (A)   a = c · \sin \alpha  
    (B)   a = c · \cos \alpha  
    (C)   b = c · \sin \beta  
    (D)   a = c · \cos \beta  

    Correct = B


     
  8. The \tan of angle \beta is given by ... 

    (A)   \tan \beta = b/a 
    (B)   \tan \beta = a/b 
    (C)   \tan \beta = b/c 
    (D)   \tan \beta = a/c 

    Correct = A


     
  9. The sin of 30^\circ is ... 

    (A)   1 
    (B)   2/3  
    (C)   1/2 
    (D)   1/4  

    Correct = C


     
  10. The cos of 60^\circ is the same as ... 
    (A)   \tan 45^\circ  
    (B)   \tan 60^\circ  
    (C)   \sin 30^\circ 
    (D)   \sin 60^\circ  

    Correct = C