In a right triangle with the hypotenuse c and the legs a and b, c^2=2ab. find the measure of each acute angle.

We know that, usually,

In this case, we also know that

We deduce that

If we subtract 2ab from both sides, we get

So, the triangle is an isosceles right triangle, and so the angles are 90-45-45

i think the amount would be $140.62

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places