📐 Right Triangle Trigonometry: Mastering sin, cos, and tan

Questions in this quiz

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1. Question 1

   In a right triangle, if the angle of interest is $30°$, the opposite side is $5$ units, and the hypotenuse is $10$ units, which trigonometric ratio is being used to relate these measurements?

2. Question 2

   In a right triangle, the tangent of an acute angle equals the ratio of the adjacent side to the opposite side.

3. Question 3

   A ladder leans against a wall, forming a $60°$ angle with the ground. If the ladder is $8$ meters long, how far is the base of the ladder from the wall?

4. Question 4

   If $\sin(\theta) = \frac{3}{5}$, then $\cos(\theta) =$ ___ (assuming $\theta$ is an acute angle in a right triangle).

5. Question 5

   The angle of elevation from a point on the ground to the top of a building is the angle between the horizontal line of sight and the line of sight to the top of the building.

6. Question 6

   A surveyor stands $50$ meters from the base of a cliff and measures the angle of elevation to the top as $35°$. Approximately how tall is the cliff? (Use $\tan(35°) \approx 0.7$)

7. Question 7

   In a right triangle with legs of length $5$ and $12$ units, the sine of the smaller acute angle is $\frac{5}{13}$ and the tangent of that angle is ___.

8. Question 8

   A ramp rises $3$ meters vertically over a horizontal distance of $12$ meters. What is the angle of inclination of the ramp, to the nearest degree?

9. Question 9

   If $\cos(\theta) = \sin(\phi)$ and both $\theta$ and $\phi$ are acute angles in a right triangle, then $\theta + \phi = 90°$.

10. Question 10

    From a point on a hillside, an observer looks down at a $20°$ angle of depression to see a marker on level ground $40$ meters away. Approximately how much higher is the observer than the marker? (Use $\tan(20°) \approx 0.364$)