Question

В треугольнике АВС АС=ВС, высота СР равна 26, cosA = корень из 2 / 2. Найдите АВ

Answer 1

sinA = кв.корень(1-cosA*cosA) = кв корень(2)/2

sinA = CH/AC

AC = CH/sinA = 26корней из 2

AH^2 = AC^2 - CH^2

AH = 26

AB = AH*2 = 52

Answer 2

Finding the Length of AB in Triangle ABC

To find the length of AB in triangle ABC, we can use the given information about the triangle's sides and angles. Let's break down the information provided:

- AC = BC (given) - Height CR = 26 - cos(A) = √2/2

To find the length of AB, we can use the cosine rule, which states that in a triangle with sides a, b, and c, and angle A opposite side a, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(A)

In our case, we want to find AB, so let's denote AB as c, AC (or BC) as a, and CR as b. Plugging in the given values, we have:

AB^2 = AC^2 + CR^2 - 2 * AC * CR * cos(A)

Since AC = BC, we can substitute BC for AC:

AB^2 = BC^2 + CR^2 - 2 * BC * CR * cos(A)

Now, let's substitute the given values:

AB^2 = BC^2 + 26^2 - 2 * BC * 26 * √2/2

Simplifying further:

AB^2 = BC^2 + 676 - 26 * BC * √2

Since AC = BC, we can substitute BC for AC again:

AB^2 = AC^2 + 676 - 26 * AC * √2

Now, we have an equation to solve for AB. However, without the specific values for AC or BC, we cannot determine the exact length of AB. We would need additional information to find the specific value of AB.

Please provide the specific values for AC or BC if you have them, and I can help you find the length of AB.