Séan is making an access ramp for a building - Junior Cycle Mathematics - Question 11 - 2016

The tangent function is defined as the ratio of the opposite side to the adjacent side. Thus:

$\tan(A) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{20}{260} = \frac{1}{13}$.

To find the angle A, we can use the inverse tangent function:

$A = \tan^{-1}\left(\frac{1}{13}\right) \approx 4.43°$

Therefore, rounding to the nearest degree, the angle A is:

$A \approx 4°$.

Yes

Reason: The angle A (4°) is less than the acceptable maximum angle (5°). Therefore, the ramp is acceptable.

Using the Theorem of Pythagoras, the relationship between the sides is given by:

$x^2 + 224^2 = 226^2$

Calculating each side: $x^2 + 50176 = 51076$

Therefore, $x^2 = 51076 - 50176 = 900$

Taking the square root gives: $x = \sqrt{900} = 30$ cm.