The diagram below shows two vertical buildings, A and B (diagram not to scale) - Junior Cycle Mathematics - Question 8 - 2022

Using the Theorem of Pythagoras:

$y^2 = 154^2 + 220^2$

Calculating the squares:

$154^2 = 23716 \\ 220^2 = 48400$

So,

$y^2 = 23716 + 48400 = 72116$

Now taking the square root:

$y = ext{sqrt}(72116) \\ y ≈ 268.54$

Rounding to the nearest metre gives:

$y ≈ 269 ext{ m}$

We can use the tangent function to find z:

$\tan(20°) = \frac{h}{154}$

where h is the height of Building B. Re-arranging gives:

$h = 154 \cdot \tan(20°)$

Calculating:

$h ≈ 154 \cdot 0.3640 ≈ 56.05$

Thus, the total height of Building B is:

$z = 220 - 56.05$

So,

$z ≈ 276 ext{ m}$

Rounding to the nearest metre gives:

$z ≈ 276 ext{ m}$