Answer:
Step-by-step explanation:
Given , start by squaring both sides to work towards isolating
:
Recall and
:
Isolate the radical:
Square both sides:
Expand using FOIL and :
Move everything to one side to get a quadratic:
Solving using the quadratic formula:
A quadratic in has real solutions
. In
, assign values:
Solving yields:
Only works when plugged in the original equation. Therefore,
is extraneous and the only solution is
Answer:
16.2
Step-by-step explanation:
The angle internal to the triangle at B is the supplement of the one shown, so is 65°. That is equal to the angle internal to the triangle at D. Since the vertical angles at C are congruent, the two triangles are similar by the AA theorem.
Corresponding sides of similar triangles are proportional, so we can write the proportion shown in the attachment:
BC/FC = DC/AC
BC = FC(DC/AC) = 21.6(7.2/9.6)
BC = 16.2 . . . . matches the first choice
