Question

short answer 6. the base of a ladder is 0.5 m from a wall of a house. the top of the ladder rests against the house 2.5 m above the ground. determine the angle the ladder makes with the house, to the nearest degree.

Explanation:

Step1: Identify the triangle sides

We have a right triangle where the adjacent side (to the angle with the house) is the height on the wall, \( a = 2.5\space m \), and the opposite side is the distance from the wall, \( b = 0.5\space m \). We use the tangent function \( \tan\theta=\frac{\text{opposite}}{\text{adjacent}} \).
\( \tan\theta=\frac{0.5}{2.5} \)

Step2: Calculate the angle

First, simplify \( \frac{0.5}{2.5}=\frac{1}{5} = 0.2 \). Then, find \( \theta=\arctan(0.2) \). Using a calculator, \( \theta\approx11.31^\circ \), which rounds to \( 11^\circ \).

Answer:

\( 11^\circ \)