Problem

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.

Solution

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.

From Solvely APP
Source: https://solvelyapp.com/problems/7192/

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