Question

A driveway is built on an incline so that it rises 1.8m and goes up a diagonal distance of 34m. What is

the angle between the ground the diagonal space? Complete and label the diagram for full marks and
state a therefore statement.

Answer 1

Here is the labeled diagram of the driveway:

/|

/ | 1.8m (Rise)

/ |

/ |

/θ |

/____| 34m (Diagonal Distance)

In the diagram, the horizontal line represents the ground, the vertical line represents the rise of the driveway (1.8m), and the diagonal line represents the diagonal distance traveled along the driveway (34m).

To find the angle θ between the ground and the diagonal space, we can use trigonometry. Specifically, we can use the inverse tangent (arctan) function, as it relates the opposite and adjacent sides.

tan(θ) = opposite side / adjacent side

In this case, the opposite side is the rise of the driveway (1.8m), and the adjacent side is the horizontal distance (34m).

tan(θ) = 1.8m / 34m

To find the value of θ, we need to take the inverse tangent (arctan) of both sides:

θ = arctan(1.8m / 34m)

Using a calculator, we can find the value of θ:

θ ≈ 3.06 degrees

Therefore, the angle between the ground and the diagonal space of the driveway is approximately 3.06 degrees.

Therefore, the statement would be: The angle between the ground and the diagonal space of the driveway is approximately 3.06 degrees.