Multiple Choice

1. In a right-angled triangle, which side is always opposite the right angle?

   The base

   The hypotenuse

   The adjacent side

   The opposite side

2. In a right-angled triangle, relative to a given acute angle, which side is across from that angle?

   The adjacent side

   The hypotenuse

   The opposite side

   The base

3. In a right-angled triangle, relative to a given acute angle, which side is next to that angle and not the hypotenuse?

   The adjacent side

   The hypotenuse

   The opposite side

   The base

4. The "SOH" part of SOHCAHTOA stands for:

   Secant = Opposite / Hypotenuse

   Sine = Opposite / Adjacent

   Sine = Opposite / Hypotenuse

   Sine = Adjacent / Hypotenuse

5. The "CAH" part of SOHCAHTOA stands for:

   Cosine = Adjacent / Hypotenuse

   Cosine = Opposite / Adjacent

   Cosecant = Adjacent / Hypotenuse

   Cosine = Opposite / Hypotenuse

6. The "TOA" part of SOHCAHTOA stands for:

   Tangent = Opposite / Adjacent

   Tangent = Adjacent / Hypotenuse

   Tangent = Opposite / Hypotenuse

   Tan = Hypotenuse / Opposite

7. In a right-angled triangle, if you know the length of the side opposite a given angle and the length of the hypotenuse, which trigonometric ratio would you use to find the angle?

   Sine

   Cosine

   Secant

   Tangent

8. In a right-angled triangle, if you know the length of the side adjacent to a given angle and the length of the hypotenuse, which trigonometric ratio would you use to find the angle?

   Tangent

   Cosecant

   Sine

   Cosine

9. In a right-angled triangle, if you know the length of the side opposite a given angle and the length of the side adjacent to that angle, which trigonometric ratio would you use to find the angle?

   Sine

   Tangent

   Cotangent

   Cosine

10. In a right-angled triangle, an angle is 30 degrees. The side opposite this angle is 5 units long. Which expression represents the length of the hypotenuse (H)?

    H = 5 / cos(30°)

    H = 5 / sin(30°)

    H = 5 * sin(30°)

    H = sin(30°) / 5

11. In a right-angled triangle, an angle is $\theta$. The hypotenuse is 10 units long. Which expression represents the length of the side opposite angle $\theta$ (O)?

    O = 10 * sin($\theta$)

    O = tan($\theta$) / 10

    O = 10 / sin($\theta$)

    O = 10 * cos($\theta$)

12. In a right-angled triangle, an angle is 45 degrees. The hypotenuse is 8 units long. Which expression represents the length of the side adjacent to angle 45 degrees (A)?

    A = 8 * sin(45°)

    A = 8 / sin(45°)

    A = 8 / cos(45°)

    A = 8 * cos(45°)

13. In a right-angled triangle, an angle is $\alpha$. The side adjacent to this angle is 7 units long. Which expression represents the length of the hypotenuse (H)?

    H = 7 / sin($\alpha$)

    H = 7 * cos($\alpha$)

    H = 7 / cos($\alpha$)

    H = sin($\alpha$) / 7

14. In a right-angled triangle, an angle is 60 degrees. The side adjacent to this angle is 4 units long. Which expression represents the length of the side opposite angle 60 degrees (O)?

    O = 4 / tan(60°)

    O = 4 * tan(60°)

    O = 4 * cos(60°)

    O = tan(60°) / 4

15. In a right-angled triangle, an angle is $\beta$. The side opposite this angle is 12 units long. Which expression represents the length of the side adjacent to angle $\beta$ (A)?

    A = 12 * tan($\beta$)

    A = 12 / sin($\beta$)

    A = 12 * sin($\beta$)

    A = 12 / tan($\beta$)

16. In a right-angled triangle, the side opposite angle X is 3 units, and the hypotenuse is 6 units. Which expression finds the measure of angle X?

    X = cos⁻¹(3/6)

    X = tan⁻¹(3/6)

    X = sin(3/6)

    X = sin⁻¹(3/6)

17. In a right-angled triangle, the side adjacent to angle Y is 8 units, and the hypotenuse is 10 units. Which expression finds the measure of angle Y?

    Y = tan⁻¹(8/10)

    Y = cos(8/10)

    Y = sin⁻¹(8/10)

    Y = cos⁻¹(8/10)

18. In a right-angled triangle, the side opposite angle Z is 7 units, and the side adjacent to angle Z is 5 units. Which expression finds the measure of angle Z?

    Z = cos⁻¹(7/5)

    Z = tan(7/5)

    Z = tan⁻¹(7/5)

    Z = sin⁻¹(7/5)

19. A ladder 15 meters long leans against a wall. The bottom of the ladder is 9 meters from the base of the wall. Let $\theta$ be the angle the ladder makes with the ground. Which expression finds $\theta$? (Assume the wall is perpendicular to the ground)

    $\theta$ = tan⁻¹(9/15)

    $\theta$ = cos⁻¹(9/15)

    $\theta$ = sin⁻¹(15/9)

    $\theta$ = sin⁻¹(9/15)

20. A flagpole casts a shadow 20 meters long. The angle of elevation from the end of the shadow to the top of the flagpole is 50 degrees. Which expression represents the height (H) of the flagpole?

    H = 20 * cos(50°)

    H = 20 * tan(50°)

    H = 20 / tan(50°)

    H = 20 * sin(50°)