# Trigonometry 1

The questions are based on the figure below: 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)   $A = a^2 + b^2 - c^2$

Correct = B

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)   $\sin 60^\circ$