📐 Introduction to Trigonometry

Questions in this quiz

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1. Question 1

   In a right triangle, if $\sin(\theta) = \frac{3}{5}$, what is the value of $\cos(\theta)$?

2. Question 2

   $\sin(30°) = \frac{1}{2}$ and $\cos(30°) = \frac{\sqrt{3}}{2}$.

3. Question 3

   If $\theta$ and $\phi$ are complementary angles (i.e., $\theta + \phi = 90°$), then $\sin(\theta) = \cos(\phi)$ and \tan(\theta) = \frac{1}{\tan(___)}.

4. Question 4

   In a right triangle, the side opposite to angle $\theta$ is 7 cm and the hypotenuse is 25 cm. What is $\tan(\theta)$ (to the nearest hundredth)?

5. Question 5

   $\tan(45°) = 1$ because in a 45-45-90 triangle, the opposite and adjacent sides are equal.

6. Question 6

   $\sin(\theta)$ is always less than $\tan(\theta)$ for any acute angle $\theta$ between $0°$ and $90°$.

7. Question 7

   A ladder leans against a wall making an angle of $60°$ with the ground. If the ladder is 10 m long, the height at which it touches the wall is ___ m.

8. Question 8

   A person standing 50 m away from a building observes the top of the building at an angle of elevation of $60°$. Assuming the observer's eye is at ground level, what is the approximate height of the building?

9. Question 9

   If $\sec(\theta) = \frac{13}{5}$, what is $\cos(\theta)$?

10. Question 10

    In triangle $ABC$, where angle $C = 90°$, $AC = 5$ cm, $BC = 12$ cm, and $AB = 13$ cm (hypotenuse). Find $\sin(A) + \cos(A)$.