Jaclynn is building a cat house for her cats. She designs a ramp from one level to the other for them to climb. The ramp length is 4 ft and the difference between the two levels is 2 feet. What is the approximate angle of elevation formed by the ramp? Round your answer to the nearest whole number (no decimals)

1 answer

To find the angle of elevation formed by the ramp, we can use the sine function in trigonometry. The sine of the angle of elevation (\(\theta\)) can be calculated using the opposite side (the vertical difference between the levels) and the hypotenuse (the length of the ramp).

Given:

  • The length of the ramp (hypotenuse) = 4 ft
  • The vertical difference between the levels (opposite side) = 2 ft

Using the sine function:

\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{2}{4} = 0.5 \]

Now, we can find the angle \(\theta\):

\[ \theta = \arcsin(0.5) \]

From trigonometric values, we know that:

\[ \arcsin(0.5) = 30^\circ \]

Thus, the approximate angle of elevation formed by the ramp is:

\[ \boxed{30} \]