What is the length of bc , rounded to the nearest tenth?

13.0 units
28.8 units
31.2 units
33.8 units

Step

In the right triangle ADB

Find the length of the segment AB

Applying the Pythagorean Theorem

we have

substitute the values

Step

In the right triangle ADB

Find the cosine of the angle BAD

we know that

Step

In the right triangle ABC

Find the length of the segment AC

we know that

solve for AC

Step

Find the length of the segment DC

we know that

we have

substitute the values

Step

Find the length of the segment BC

In the right triangle BDC

Applying the Pythagorean Theorem

we have

substitute the values

therefore

the answer is

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.