Question

4. Радіус кола , вписаного в основу правильної піраміди, дорівнює 5 корінь із 3 сантиметрів. Знайдіть кут нахилу бічної грані піраміди до основи піраміди, якщо висота піраміди дорівнює 5 см Розгорнута відповідь!!

Answer 1

Ответ:

Кут нахилу бічної грані до основи дорівнює 30°

Объяснение:

H=5см; r=5√3см

tga=H/r=5/5√3=1/√3

а=arctg1/√3=30°

Answer 2

Calculation of the Inclination Angle of the Pyramid's Lateral Face to the Base

To find the inclination angle of the lateral face of the pyramid to the base, we can use trigonometry. Let's denote the radius of the circle inscribed in the base of the pyramid as r (which is given as 5√3 cm) and the height of the pyramid as h (which is given as 5 cm).

The radius of the inscribed circle is related to the height and the inclination angle of the lateral face by the following trigonometric relationship:

r = h * tan(θ)

where θ is the inclination angle of the lateral face.

To find the inclination angle, we can rearrange the equation as follows:

θ = arctan(r / h)

Now, let's substitute the given values into the equation and calculate the inclination angle.

r = 5√3 cm (given) h = 5 cm (given)

Using the equation, we can calculate the inclination angle:

θ = arctan(5√3 / 5)

Calculating this expression gives us:

θ ≈ 60°

Therefore, the inclination angle of the lateral face of the pyramid to the base is approximately 60 degrees.

Please note that the above calculation assumes that the pyramid is a regular pyramid with a regular polygon as its base.