Answer :
Final answer:
In this Mathematics problem, the concept of similar triangles and trigonometric ratios was used to find the differences in shadow lengths at two different sun altitudes. The shadow at a Sun altitude of 45 degrees was 50m. When the Sun's altitude was 30 degrees, the shadow length was 50*√3m. The difference, or 'x', thus came out to be approximately a.36.6m.
Explanation:
In Mathematics, problems like this are often solved using the properties of similar triangles. Attributes of a shadow and a triangle share certain aspects that we can apply.
First, we have to remember the concept of trigonometric ratios. For a 45-degree angle, the ratio of the height to the shadow is 1:1, meaning the shadow length is equal to the height. Therefore, when the altitude of the sun is 45°, the shadow's length is 50m.
For a 30-degree angle, the ratio of the height to the shadow is 1:√3, meaning the shadow length is √3 times the height. Therefore, when the altitude of the sun is 30°, the shadow's length is 50√3 m.
Now, to find 'x', which is how much shorter the shadow is at 45° than at 30°, we subtract the two shadow lengths: 50√3 - 50 = 50(√3 - 1). So, 'x' is approximately 36.6 m.
Learn more about Trigonometry here:
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