Answer:
1) x = 5√3, y = 5
2) x = 16, y = 8
3) x = 10, y = 5
4) m = 9√15/10, n = 9√5/10
5) x = 3√3/2, y = 3/2
6) x = 6√5, y = 3√5
7) x = 5, y = 5
8) x = 5√2, y = 5
9) a = 2, b = √2
10) m = 10√6/3, n = 5√6/3
Step-by-step explanation:
For special right triangles, there is a certain side ratio that applies due to the angle measurements which are opposite of the corresponding angles.
For 30° - 60° - 90° triangles (Scalene Right), we can use x as a marker for the side opposite of 30°, the side opposite of the 60° angle will be x√3, and the side opposite of the 90° angle will be 2x.
For 45° - 45° - 90° triangles (Isosceles Right),
Both 45° angles can be thought of as x, and the 90° angle can be thought of as x√2.
This is all computed as a result of the trigonometric functions:
SOH CAH TOA.
This is a shortcut for these specific triangles.
If you do not have the side marked as x, just do the inverse operation to get it.
90° is always opposite of the hypotenuse (longest side of a triangle; looks like a slant)