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Two friends are building a skate-board ramp - Junior Cycle Mathematics - Question 11 - 2022
Question 11
Two friends are building a skate-board ramp. They each have a different design for the ramp. Tracey draws the following diagram as part of her design for the ramp. ... show full transcript
Worked Solution & Example Answer:Two friends are building a skate-board ramp - Junior Cycle Mathematics - Question 11 - 2022
Step 1
Construct a scale diagram of this part of the design for the ramp in the grid below.
Answer
To construct the scale diagram, we first note that the scale is 1:50. Thus, to obtain the lengths for the scaled diagram, we need to multiply the original lengths by 50 and then divide by 100 to convert them appropriately. The original lengths given in the diagram are 3.5 cm and 2 cm for the triangle. After scaling, we have:
- For side 1 (3.5 cm): ( \frac{3.5 \times 50}{100} = 1.75 ) cm
- For side 2 (2 cm): ( \frac{2 \times 50}{100} = 1 ) cm
The final scale diagram will include accurate representations of these lengths in the provided grid, ensuring each side is accurately measured with a ruler.
Step 2
Step 3
Use the Theorem of Pythagoras to work out the length of the side B in Sinéad’s design.
Answer
To find the length of side B, we apply the Pythagorean theorem, which states that in a right triangle:
In this case, we have:
- The hypotenuse (c) = 180 cm
- One side (a) = 96 cm
We rearrange to find b (side B):
( B^2 = 180^2 - 96^2 ) ( B^2 = 32400 - 9216 ) ( B^2 = 24184 ) ( B = \sqrt{24184} \approx 155.5 ) cm. Thus, the length of side B is approximately 155.5 cm.
Step 4
Use your calculator to find the size of the angle C, correct to the nearest degree.
Answer
To find the angle C, we use the tangent function defined as follows:
Using a calculator: ( C = tan^{-1}\left(\frac{96}{180}\right) \approx 28.07 ) degrees. Rounded to the nearest degree, angle C is 28 degrees.