High School

We appreciate your visit to A tower is 50 m high Its shadow is x meters shorter when the sun s altitude is 45 than when it is 30 Find. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

A tower is 50 m high. Its shadow is x meters shorter when the sun's altitude is 45° than when it is 30°. Find 'x', correct to the nearest cm.

A. 36.6 m
B. 32.5 m
C. 30.5 m
D. 31.5 m

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:

https://brainly.com/question/31896723

#SPJ11

Thanks for taking the time to read A tower is 50 m high Its shadow is x meters shorter when the sun s altitude is 45 than when it is 30 Find. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada