Question 66 - Problems - Chapter 1¶

Problem:¶

You want to estimate the height of a sky-scraper from the ground. To do so, you walk 150 steps (75m) away from the vertical wall, and, usig a protractor, measure an angle of 78° that the line of sight to the top of the skyscraper makes with the horizontal.

Pollished crystal-grid

Question:¶

How tall is the skyscraper?

How many significant figures are in your result?

Solution:¶

Since the atoms are spherical we can use the ratio without having to know the dimensions.

$$ \textrm{Height}=\textrm{Distance}*\tan \left(\widehat{a}\right)) $$

In [1]:

# Calculations
import numpy as np
from astropy import units as u

Distance = 75
a = 78 * u.degree
Height = Distance * np.tan(a)
print(f'The calculated height of the building is {Height:.0f} m')

The calculated height of the building is 353 m

We can only use two significant figures so the estimated height is $\text{ 350 m }(\pm10m)$

سُوۡرَةُ حٰمٓ السجدة / فُصّلَت
ثُمَّ اسْتَوَىٰ إِلَى السَّمَاءِ وَهِيَ دُخَانٌ فَقَالَ لَهَا وَلِلْأَرْضِ ائْتِيَا طَوْعًا أَوْ كَرْهًا قَالَتَا أَتَيْنَا طَائِعِينَ ﴿١١
فَقَضَاهُنَّ سَبْعَ سَمَاوَاتٍ فِي يَوْمَيْنِ وَأَوْحَىٰ فِي كُلِّ سَمَاءٍ أَمْرَهَا ۚ وَزَيَّنَّا السَّمَاءَ الدُّنْيَا بِمَصَابِيحَ وَحِفْظًا ۚ ذَٰلِكَ تَقْدِيرُ الْعَزِيزِ الْعَلِيمِ ﴿١٢

Surah Fussilat: Thereafter turned He to the heaven and it was as smoke, and said Unto it and Unto the earth: come ye twain, willingly or loth. They said: we come willingly. (11) Then He decreed them as seven heavens in two days, and revealed Unto each heaven the command thereof; and We bedecked the nether heaven with lamps and placed therein a guard. That is the ordinance of the Mighty, the Knower. (12)

De hemelen en aarde (waren) een samenhangende massa. Wij hebben ze toen van elkaar gescheiden… Wij hebben de hemel tot een beschermend dak gemaakt … en de dag en de nacht, de zon en de maan geschapen. (Koran 41 11:12)