Question

identifying trig ratios (diagram), level 1
score: 4/10 penalty: none
question
express tan w as a fraction in simplest terms.
answer attempt 1 out of 2
tan w = submit answer

Explanation:

Step1: Find the length of the opposite side

In a right - triangle, for angle \(W\), the side opposite to angle \(W\) is \(XY\). Using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) (where \(c = 5\) and \(b = 4\)), we have \(a=\sqrt{c^{2}-b^{2}}=\sqrt{25 - 16}=\sqrt{9}=3\). So, the length of the side opposite to angle \(W\) (\(XY\)) is \(3\).

Step2: Recall the tangent ratio formula

The tangent of an angle in a right - triangle is defined as \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For angle \(W\), the opposite side \(= 3\) and the adjacent side \(= 4\).

Answer:

\(\frac{3}{4}\)