A ladder (length 314 cm) is leaning up against a wall. The length between the ladder and the wall is 1.54 m. At what angle is the ladder leaning up against the wall? Round your answer to 2 d.p.
In situations like this I would always find it best to draw a diagram with all the information we know labelled on it. Firstly, however, notice that our measurements are in different units. You can convert them both into metres or centimetres, lets convert into metres so we aren't dealing with big numbers, if would prefer no decimals, you could always convert into centimetres! We know there are 100cm in a metre, therefore 314 cm / 100 will give us the number of metres = 3.14 m.Now to calculate our angle. This question is asking us to use trigonometric functions (sin, cos and tan). SOH CAH TOA will help us with this question. From the diagram, we know we have the length of the HYPOTENUSE and the ADJACENT. This tells us we need to use cosine for this question. So, lets substitute into the formula we get from SOH CAH TOA. cos(angle) = 1.54/3.14. Now we need to rearrange. When calculating angles using our trig functions, we know we will need to use the trig inverse button on our calculators, this is noted as cos-1 . So cos-1(1.54/3.14) will give us our angle. The answer here is 60.63o to 2 decimal places.
