+1262 we can use the pythagorenas theorem to find the altitude is 60 and we have te equation 60^2+x^2=y^2 and (x+25)^2-65^2=y^2 where y is the base
In the small right triangle on the RHS with sides of 65 and 25, wil find the altitude by Pythagoras's Theorem:
65^2 =25^2 + A^2
A =sqrt(3600) =60
The measure of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean of the measures of the two segments of the hypotenuse.
Sqrt(25x) =60
5sqrt(x) =60 Divide both sides by 5
sqrt(x) =12 Square both sides
x = 144
I think Alan made a typo. You can't solve for x in the last equation!
Cos(25/65) = 65 /(x + 25) - Now you can solve for x
169 =x + 25
x =169 - 25 = 144
Hello, Guest!
Alan's equation is solvable; it just takes more time, but the result is the same.
65 / x+25 = 25 / 65
Step 1: Cross-multiply.
65 * 65 = 25 * x+25
4225 = 25x + 625
Step 2: Flip the equation.
25x + 625 = 4225
Step 3: Subtract 625 from both sides.
25x + 625−625 = 4225−625
25x = 3600
Step 4: Divide both sides by 25.
25x / 25 = 3600 / 25
x = 144
