Question

identifying trig ratios (diagram), level 1
score: 2/10 penalty: none
question
find the value of cos f rounded to the nearest hundredth, if necessary.
answer attempt 1 out of 2
cos f =

Explanation:

Step1: Find the length of \(FG\)

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). Here \(c = 34\), \(b = 16\), and \(a=FG\). So \(FG=\sqrt{34^{2}-16^{2}}=\sqrt{(34 + 16)(34 - 16)}=\sqrt{50\times18}=\sqrt{900}=30\).

Step2: Calculate \(\cos F\)

The cosine of an angle in a right - triangle is defined as \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). For \(\angle F\), the adjacent side to \(\angle F\) is \(FG = 30\) and the hypotenuse is \(FH=34\). So \(\cos F=\frac{FG}{FH}=\frac{30}{34}\approx0.88\).

Answer:

\(0.88\)