Question

what is the perimeter of $\triangle def$ to the nearest tenth?a. 19.4b. 20.1c. 25.3d. 43.3

Explanation:

Step1: Find side DF (adjacent to ∠D)

Use cosine of ∠D:
$\cos(38^\circ) = \frac{DF}{DE}$
$DF = 18 \times \cos(38^\circ) \approx 18 \times 0.7880 = 14.184$

Step2: Find side EF (opposite to ∠D)

Use sine of ∠D:
$\sin(38^\circ) = \frac{EF}{DE}$
$EF = 18 \times \sin(38^\circ) \approx 18 \times 0.6157 = 11.083$

Step3: Calculate perimeter

Sum all sides:
$\text{Perimeter} = DE + DF + EF = 18 + 14.184 + 11.083$

Answer:

D. 43.3