Question

identifying trig ratios (diagram), level 1
score: 0/10 penalty: none
question
express tan g as a fraction in simplest terms.
answer

Explanation:

Step1: Recall the tangent ratio formula

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For angle \(G\), the side opposite to \(G\) is \(HI = 24\), and the side adjacent to \(G\) is \(GH=32\) (using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 40\), \(b = 24\), then \(a=\sqrt{40^{2}-24^{2}}=\sqrt{(40 + 24)(40 - 24)}=\sqrt{64\times16}=32\)).

Step2: Calculate \(\tan G\)

\(\tan G=\frac{HI}{GH}=\frac{24}{32}\).

Step3: Simplify the fraction

Divide both the numerator and the denominator by their greatest common divisor. The GCD of 24 and 32 is 8. \(\frac{24\div8}{32\div8}=\frac{3}{4}\).

Answer:

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