Question

applying a trigonometric ratio to find a side length. what is the value of d to the nearest hundredth? d =

Explanation:

Step1: Identify the trig - ratio

In right - triangle $\triangle DEF$ with right - angle at $E$, if we consider the angle $\angle D = 42^{\circ}$ and the side $DE = 7.2$, and we want to find the side $EF=d$. We use the tangent ratio since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\tan D=\frac{EF}{DE}$.

Step2: Substitute the values

We know that $\tan42^{\circ}\approx0.9004$ and $DE = 7.2$. Substituting into the formula $\tan D=\frac{EF}{DE}$, we get $0.9004=\frac{d}{7.2}$.

Step3: Solve for $d$

Multiply both sides of the equation by $7.2$: $d = 7.2\times\tan42^{\circ}$. Then $d=7.2\times0.9004 = 6.48288\approx6.48$.

Answer:

$6.48$