First vector orthogonal<span> to ⟨−</span>3<span>,4</span>
Answer: y = 16.5
Step-by-step explanation:
We would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
Considering triangle BCD,
BD² = 14² - 8²
BD² ° 196 - 64 = 132
BD = √132
Considering triangle ABD,
AB² = BD² + y²
AB² = (√132)² + y²
AB² = 132 + y²- - - - - - - - - - 1
Considering triangle ABC,
(8 + y)² = AB² + BC²
(8 + y)² = AB² + 14²
(8 + y)² = AB² + 196
AB² = (8 + y)² - 196- - - - - - - -2
Substituting equation 1 into equation 2, it becomes
132 + y² = (8 + y)² - 196
y² - (8 + y)² = - 196 - 132
y² - (64 + 16y + y²) = - 328
y² - 64 - 16y - y2 = - 328
- 16y = - 328 + 64
- 16y = - 264
y = - 264/- 16
y = 16.5
The answer is -18y = 1 because the 5s cancel out
