Question

Determine the measure of ∠θ using a trigonometric ratio.Question 4 options:A) 17.38°B) 12.54°C) 1.00°D) 45.10°

Answer 1

The given triangle has a right angle, which means it is a right triangle.

The ratio of the right triangle sides are related to the functions sine, cosine and tangent. In this case, the angle we want is adjacent to a leg of measure 12 and we know that the hypotenuse of the triangle is 17. This means we can use the cosine of the angle:

$\cos \theta=\frac{adjacent\, leg}{hypotenuse}=\frac{12}{17}$

Now, taking the arccos, we get:

$\theta=\arccos (\frac{12}{17})=45.0991\ldots\approx45.10\degree$

Which corresponds to alternative D.