A pole casting a shadow 49 feet long with an angle of elevation of the sun of 44.8 degrees is 50 feet tall. (47.98 rounded to two places)
Tangent (theta) = opposite / adjacent
Tangent (44.9) = X / 49
X = 47.98
This does not take into account the curvature of the earth, but the error in this example is inconsequential, specifically an elevation error of about 0.015 percent.
By means of trigonometry if you know the angle of elevation or by comparing it with a nearby object if you know its height and shadow length.
18.6 m/52.6 degrees tan= 14.2
Using tangent ratio for a right angle triangle: tan(48.4)*7.42 = 8.357 m which is the height of the flag pole rounded to 3 decimal places
Use the tangent angle of elevation which works out as 31.7497 degrees to four decimal places
Using trigonometry the angle of elevation is 77 degrees rounded to the nearest degree
When the angle of elevation equals 45 degrees. tan-1(1) = 45 degrees.
The flagpole is 15.92 metres, approx.
Angle of elevation: tan-1(100/130) = 37.6 degrees rounded to one decimal place
If you also know its shadow then you can work out the angle of elevation
Using trigonometery if you know the length of its shadow and angle of elevation
By means of trigonometry if you know the angle of elevation or by comparing it with a nearby object if you know its height and shadow length.
18.6 m/52.6 degrees tan= 14.2
Using the sine rules in trigonometry the height of the mountain works out as 3704 meters in height to the nearest whole number.
It is: tan(52)*9 = 11.519 meters rounded to three decimal places
Using the tangent ratio height of telegraph pole is 55 feet to the nearest integer.
Using tangent ratio for a right angle triangle: tan(48.4)*7.42 = 8.357 m which is the height of the flag pole rounded to 3 decimal places
If the angle of elevation is 32 degrees then using the tangent ratio in trigonometry the height of the tree is 18.75 feet rounded up to two decimal places