ACT Math: Trigonometry Drill 1, Problem 1. What is the length of y?
|Foreign Language||Arabic Subtitled|
|Product Type||ACT Math|
|Trigonometry||SOHCAHTOA (values and properties of trig functions)|
Solving right triangles
Trigonometric relations in right triangles
Since we're told that x equals 10, we can set up a ratio that looks like this. And we
cross multiply to solve for z.
We get 10 times 5 equals 50...and 3 times z as 3z. So now divide both sides
by 3 and we get that z equals around 16.7. And now that we have two side lengths of a
right triangle, we can use the Pythagorean Theorem to solve for y.
So now we can just plug in our values.
10 squared plus y squared equals 16.7 squared. 100 plus y squared equals 278.89. Subtract
100 from both sides, and we get that y squared equals 178.89.
Take the square root of both sides, and we get that y equals plus or minus 13.3.
Sides can't be negative...
...so the answer is 13.3. So it's A.