A $5.7 \mathrm{~m}$ long ladder is leaning against a wall. The wall stands perpendicular to the ground. The base of the ladder is $1.5 \mathrm{~m}$ away from the wall.
Work out the size of the acute angle that the ladder makes with the ground. Give your answer in degrees to 1 d.p.
Answer
Use the tangent function to find the angle between the ladder and the ground: \(\text{angle} = \arctan(\frac{b}{a})\). Convert the angle from radians to degrees and round to 1 decimal place. \(\boxed{74.7}\) degrees.
Step 1 ：Use the Pythagorean theorem to find the height of the ladder on the wall: \(b^2 = c^2 - a^2\), where \(a = 1.5\) and \(c = 5.7\). Calculate \(b\) as the square root of \(b^2\).
Step 2 ：Use the tangent function to find the angle between the ladder and the ground: \(\text{angle} = \arctan(\frac{b}{a})\). Convert the angle from radians to degrees and round to 1 decimal place. \(\boxed{74.7}\) degrees.
