Question

Высота дерева 6,4 метра. На расстоянии 3,7 метра от дерева стоит буссоль на стойке высотой 1 метр. Под каким углом видна макушка дерева от поверхности земли? На каком расстоянии макушка дерева от буссоли?

Answer 1

АВ=6,4м - высота дерева

СD=1м  - высота буссоли

AD=3,7м - расстояние от дерева до буссоли

AD||KC=3,7м

Δ АВD - прямоугольный

ВD - гипотенуза

BD=√6,4²+3,7²= 7,4(м) 

АВ/ВD=sin<ABC

sin<ABC=6,4/7,4≈0,086

<ABC=84° - угол, под которым видна макушка дерева от поверхности земли

Δ ВКС - прямоугольный

ВК=6,4-1=5,4(м)

ВС=√5,4²+3,7²≈6,5(м) - расстояние от макушки дерева до буссоли

Answer 2

Calculation of the Angle and Distance

To calculate the angle at which the top of the tree is visible from the surface of the ground and the distance between the top of the tree and the compass, we can use trigonometry.

Let's denote the height of the tree as h (6.4 meters), the distance from the tree to the compass as d (3.7 meters), and the height of the compass stand as c (1 meter).

To find the angle at which the top of the tree is visible, we can use the tangent function:

tan(angle) = h / (d + c)

Substituting the given values:

tan(angle) = 6.4 / (3.7 + 1)

Simplifying:

tan(angle) = 6.4 / 4.7

To find the angle, we can take the inverse tangent (arctan) of both sides:

angle = arctan(6.4 / 4.7)

Using a calculator, we find that the angle is approximately 54.9 degrees.

To find the distance between the top of the tree and the compass, we can use the sine function:

sin(angle) = h / distance

Substituting the given values:

sin(54.9) = 6.4 / distance

Simplifying:

distance = 6.4 / sin(54.9)

Using a calculator, we find that the distance is approximately 7.8 meters.

Therefore, the top of the tree is visible at an angle of approximately 54.9 degrees from the surface of the ground, and it is located approximately 7.8 meters away from the compass.

Please note that these calculations assume a flat surface and no obstructions between the compass and the tree.