Not enough information has been given to solve this problem such as: What is the angle of elevation?
If a 15-meter flagpole casts a shadow that is 35 meters long, how long is the shadow cast by a tree that is 21 meters high?
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If we assume the the flagpole makes a 90 degree angle with the ground, then the angle of elevator for the sun is 34.778°
First, find the ratio of fencepost-height : shadow which is 1.6 : 2.6 . This can also be written as a fraction, 1.6/2.6 . Then, multiply the flagpole's shadow by this ratio: 31.2 x 1.6/2.6 = 19.2 The flagpole is 19.2m high. The trigonometry way: On the imaginary right angled triangle formed by the fencepost and its shadow, let the angle at which the hypotenuse meets the ground = θ sinθ = 1.6/2.6 sinθ = /31.2 x/31.2 = 1.6/2.6 2.6x = 31.2 * 1.6 = 49.92 x = 19.2 The flagpole is 19.2m high.
Use the tangent ratio: tan = 22.5/34 = 45/68 tan-1(45/68) = 33.49518467 degrees Angle of elevation = 33o29'42.66''
Tangent (theta) is cosine / sine, or Y / X.Tangent (theta) is 40 / 58Theta = 34.6 degreesSince we are dividing cosine by sine, the hypotenuse does not matter as it cancels out.
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1.8 meters. The ratio of object to shadow is 10:6. Therefore if the object is 3, the shadow is 1.8 ( 6/10x3).
As the question is stated, Tom is standing IN THE TOWER'S SHADOW. If so, then Tom can't cast a shadow of his own, because he is not illuminated. Let's assume the question means to imply that Tom's shadow is measured AT THE SAME TIME that the shadow of the tower is measured, and kind of NEAR the tower, so that the sun casts both shadows from the same place in the sky. If this is a valid assumption, then the tower is 12 meters tall.
It is approx 36.6 ft.
To cast a 19 foot shadow the building would have to be 26.91 feet tall. Each foot of building/tree casts 8.47 inches of shadow.
Required angle has a tangent of 7.6/6.1 ie 1.249. This is 51.25 degrees.
It is: tan(52)*9 = 11.519 meters rounded to three decimal places
28 feet
21
The height of the tree is in direct proportion to the pole and its shadow
A 1 foot shadow I think.
40 ft