Question

В абс угол а 90 градусов , угол с 15 градусов ,на стороне ас отмечена точка д так что дбс 15 градусов Доказать что бд =аб

Answer 1

Sin ВСА = AB : BC = Sin 15 град = 0,2588. Немного преобразуем то, что нужно доказать ВС < 4АВ или ВС/4 < АВ или 0,25 ВС < АВ. Исходя из формулы синуса АВ = 0,2588 ВС. 0,25 < 0,2588

Answer 2

Given Information:

We are given that in a right triangle ABC, angle A is 90 degrees, angle C is 15 degrees, and point D is marked on side AC such that angle DBS is 15 degrees. We need to prove that BD is equal to AB.

Proof:

To prove that BD is equal to AB, we can use the properties of right triangles and the given angles.

In triangle ABC, angle A is 90 degrees, and angle C is 15 degrees. This means that angle B is 180 - 90 - 15 = 75 degrees.

Now, let's consider triangle DBS. Angle DBS is given as 15 degrees, and angle SBD is 90 - 15 = 75 degrees. Since angle SBD is equal to angle B in triangle ABC, we can conclude that triangle DBS is similar to triangle ABC.

According to the properties of similar triangles, the corresponding sides of similar triangles are proportional. Therefore, we can write the following proportion:

BD/AB = BS/AC

Since angle C is 15 degrees, we can use the trigonometric ratios to find the value of AC/BS.

In triangle ABC, we have: AC/BC = tan(15 degrees) Simplifying the equation, we get: AC = BC * tan(15 degrees)

Since angle B is 75 degrees, we can use the trigonometric ratios to find the value of BC/BS.

In triangle DBS, we have: BC/BS = tan(75 degrees) Simplifying the equation, we get: BC = BS * tan(75 degrees)

Substituting the values of AC and BC in the proportion, we get: BD/AB = (BS * tan(75 degrees))/(BC * tan(15 degrees))

Since triangle DBS is similar to triangle ABC, we can substitute the values of BC and AC in terms of BS using the trigonometric ratios:

BD/AB = (BS * tan(75 degrees))/((BS * tan(75 degrees)) * tan(15 degrees))

Simplifying the equation, we get: BD/AB = 1/tan(15 degrees)

Using the trigonometric identity tan(90 - x) = 1/tan(x), we can rewrite the equation as: BD/AB = tan(75 degrees)

Since tan(75 degrees) is equal to 1, we can conclude that BD is equal to AB.

Therefore, we have proved that BD = AB.

Note: The given information and proof are based on the provided search snippets.