ACT Math 5.2 Trigonometry
ACT Math: Trigonometry Drill 5, Problem 2. What is the measure of Angle x?
|Foreign Language||Arabic Subtitled|
|Geometry||Right Triangles and Trigonometry|
|Product Type||ACT Math|
|Trigonometry||SOHCAHTOA (values and properties of trig functions)|
Solving right triangles
Trigonometric relations in right triangles
According to SOHCAHTOA,
the sine is opposite over hypotenuse.
So if sin(x) equals one over two, one is the length of the side opposite angle x and two
is the adjacent side, or the hypotenuse. Using the Pythagorean theorem, we can solve
for the length of the missing leg.
1 squared plus the leg squared equals 2 squared. This simplifies to 1 plus the leg squared
Subtract 1 from both sides, and we get that the leg squared equals 3. Take the square
root of both sides, and the leg equals square root of 3.
This makes the ratio of the sides, 1 to the square root of 3 to 2, making this a special 30-60-90 triangle.
x, the angle opposite the smallest side length, is the smallest angle, or 30 degrees.
So it's A.