Bookwork code: $2\mathrm{C}$
Calculator
allowed
A $5.3\mathrm{m}$ long ladder is leaning against a wall. The wall stands perpendicular to the ground. The base of the ladder is $1.6\mathrm{m}$ 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.
$<$ Previous
Watch video
Answer

Step 1 ：Given that the length of the ladder (hypotenuse) is $5.3\mathrm{m}$ and the distance from the wall to the base of the ladder (adjacent side) is $1.6\mathrm{m}$.

Step 2 ：We can use the cosine function to find the angle. The formula for cosine is $\cos (\theta )=\frac{\text{adjacent}}{\text{hypotenuse}}$.

Step 3 ：Substitute the given values into the formula: $\cos (\theta )=\frac{1.6}{5.3}=0.30188679245283023$.

Step 4 ：To find the angle, we use the arccosine function on the result: $\theta =\arccos (0.30188679245283023)=1.2641251600418995$ radians.

Step 5 ：Convert the angle from radians to degrees: $\theta =1.2641251600418995\times \frac{180}{\pi }=72.4$ degrees.

Step 6 ：Final Answer: The acute angle that the ladder makes with the ground is $\boxed{{\displaystyle 72.4}}$ degrees.