Question

solving for angle measures of right triangles
applying a trigonometric ratio to find a side length
what is the value of d to the nearest hundredth?

Explanation:

Step1: Identify the trigonometric ratio

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

Step2: Solve for d

Multiply both sides of the equation by 7.2. $d = 7.2\times\tan(42^{\circ})$.
We know that $\tan(42^{\circ})\approx0.9004$.
$d=7.2\times0.9004 = 6.48288$.

Step3: Round to the nearest hundredth

Rounding 6.48288 to the nearest hundredth gives $d\approx6.48$.

Answer:

$6.48$