Answer:
x = <u>16</u> units
Step-by-step explanation:
∆ABC is a 45-45-90 triangle, and ∆BCD is a 30-60-90 triangle.
If side opposite of 90° [∆] = x, side opposite of 45° [∆] = x / √2 = x √ 2 / 2.
Given side AC is opposite of 90° [∆ABC] = 32 √ 2, side opposite of 45° [∆ABC] = 32 √ 2 / √ 2 = 32 which is AB or BC.
Since side BC is part of BCD.
Side opposite of 90° [∆BCD] = BC = 32.
Since x is opposite of 30° [∆BCD].
x = Side opposite of 90° [∆BCD] / 2 = 32 / 2 = 16.
Answer:
<h2>d=(14,0)</h2>
Step-by-step explanation:
<h2>√(7-(-7))^+(4/19-4/19)^</h2><h2>√(7+7)^+(0)^</h2><h2>√(14)^+0</h2><h2>= 14</h2>
Answer:
Natalie has 4 apples left
Step-by-step explanation:
one bag is 8 apples and only has 4 left so it cant fill another bag let alone 4, so a is out. Natalie has 4 apples, not 4 bags, so there goes B. The only one left is C Natalie has apples left after filling 51 bags.
Answer:
m<FED=60, m<DEN=120
Step-by-step explanation:
m<FED=60
This is because <GEN and <FED are vertical angles.
Vertical angles are always congruent.
Vertical angles are formed by a pair of intersecting lines, and are the angles directly across from one another.
m<DEN=120
This is because <DEN and <GEN are supplementary.
Supplementary angles add up to 180 degrees.
We know this because a straight line is always 180 degrees.
So:
m<DEN+m<GEN=180
m<DEN+60=180
m<DEN=120
Since 
and 
, we can rewrite the right side of the equation as
Using the identity 
, we can subtract 
from either side to obtain the identity 
substituting that into our previous expression, the right side of our equation simply becomes
We can now write our whole equation as
Adding 2 to both sides:
dividing both sides by 3:
When 0 ≤ x ≤ π, tan x can only be equal to 1 when sin x = cos x, which happens at x = π/4, and it can only be equal to -1 when -sin x = cos x, which happens at x = 3π/4
