Trigonometric function

Question

Answer 1

θ = arctan(15/8) ≅ 61.9275°

cos(61.9275°) ≅ 0.470588

Answer 2

Good morning!

The tangent of an angle within a triangle is found when we divide the length of the angle's opposite side by the length of the angle's adjacent side.

tangent = opposite / adjacent

We know from the problem that the opposite side must be 15 units and the adjacent side must be 8 units. That's given to us by the fraction provided for the value of the tangent!

OK, so now we can figure out the length of the hypotenuse. Use the Pythagorean theorem.

a² + b² = c²

8² + 15² = 64 + 225 = 289

To find the hypotenuse, we need to take the square root of that sum. Remember - when we added the squares of the two sides, we got the square of the hypotenuse.

The square root of 289 is 17. So the hypotenuse of our triangle is 17.

Now we can calculate the cosine of our angle.

cos = adjacent / hypotenuse

cos = 8 / 17