The interception point or solving for X?
Answer:
![\frac{4}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B5%7D)
Step-by-step explanation:
Given
sinΘ =
= ![\frac{opposite}{hypotenuse}](https://tex.z-dn.net/?f=%5Cfrac%7Bopposite%7D%7Bhypotenuse%7D)
Then the hypotenuse = 5 and one leg of the right triangle is 3
Using Pythagoras' identity to find the second leg (x)
x² + 3² = 5²
x² + 9 = 25 ( subtract 9 from both sides )
x² = 16 ⇒ x = 4
cosΘ =
= ![\frac{4}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B5%7D)
we have
![6 = x^{2}- 10x](https://tex.z-dn.net/?f=%206%20%3D%20x%5E%7B2%7D-%2010x%20%20)
Complete the square. Remember to balance the equation by adding the same constants to each side
![x^{2}- 10x+25=6+25](https://tex.z-dn.net/?f=%20x%5E%7B2%7D-%2010x%2B25%3D6%2B25%20%20)
![x^{2}- 10x+25=31](https://tex.z-dn.net/?f=%20x%5E%7B2%7D-%2010x%2B25%3D31%20%20)
Rewrite as perfect squares
![(x-5)^{2}=31](https://tex.z-dn.net/?f=%20%28x-5%29%5E%7B2%7D%3D31%20%20)
![(x-5)=(+/-)\sqrt{31}\\ x1=5+\sqrt{31} \\ x2=5-\sqrt{31}](https://tex.z-dn.net/?f=%20%28x-5%29%3D%28%2B%2F-%29%5Csqrt%7B31%7D%5C%5C%20x1%3D5%2B%5Csqrt%7B31%7D%20%5C%5C%20x2%3D5-%5Csqrt%7B31%7D%20%20)
therefore
the answer is
the solutions are
![x1=5+\sqrt{31} \\ x2=5-\sqrt{31}](https://tex.z-dn.net/?f=%20x1%3D5%2B%5Csqrt%7B31%7D%20%5C%5C%20x2%3D5-%5Csqrt%7B31%7D%20)