Bookwork code: $2 \mathrm{C}$
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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.
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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 \(\boxed{72.4}\) degrees.