The diagram below shows Tom's ladder leaning against a vertical wall - Junior Cycle Mathematics - Question 10 - 2018

Upon evaluating the ratios:

• The adjacent side is the distance from the wall: 3 m
• The hypotenuse is the length of the ladder: 5 m

Thus, we find:

$\cos B = \frac{3}{5}$

This means the correct statement is:

• cos $B = \frac{3}{5}$ (Tick this box)

To find the angle $B$, we use the cosine inverse:

$B = \cos^{-1}\left(\frac{3}{5}\right)$

Using a calculator, we calculate:

$B \approx 53.1^{\circ}$

Thus, the size of angle $B$ is approximately:

$B = 53^{\circ}$ (to one decimal place)

For the triangles formed by the ladders and the wall, we have:

From Cameron's ladder, the height is 6 m and the distance from the wall is 5.8 m. The ratio is:

$\frac{6}{5.8} = \frac{x}{9}$

Cross-multiplying gives:

$6 \cdot 9 = 5.8 \cdot x$

Calculating gives:

$54 = 5.8x$

Then, solving for $x$:

$x = \frac{54}{5.8} \approx 9.31 ext{ m}$

Hence the vertical height of Jamie's ladder is:

$x \approx 9.31 ext{ m}$