Question

solve the given right triangle for its missing angle and side measures. note figure not drawn to scale. a. m∠d = 55°, de ≈ 8.40 units, df ≈ 14.65 units b. m∠d = 35°, de ≈ 8.40 units, df ≈ 14.65 units c. m∠d = 55°, de ≈ 4.40 units, df ≈ 13.65 units d. m∠d = 35°, de ≈ 8.40 units, df ≈ 13.65 units

Explanation:

Step1: Find the missing angle

In a right - triangle, the sum of the two non - right angles is 90°. Given one non - right angle $\angle F = 35^{\circ}$, then $\angle D=90^{\circ}-\angle F$. So, $\angle D = 90^{\circ}-35^{\circ}=55^{\circ}$.

Step2: Find side $DE$

We know that $\tan F=\frac{DE}{EF}$. Given $EF = 12$ units and $\angle F = 35^{\circ}$, then $DE=EF\times\tan F$. So, $DE = 12\times\tan35^{\circ}\approx12\times0.7002\approx8.40$ units.

Step3: Find side $DF$

We know that $\cos F=\frac{EF}{DF}$. Given $EF = 12$ units and $\angle F = 35^{\circ}$, then $DF=\frac{EF}{\cos F}=\frac{12}{\cos35^{\circ}}\approx\frac{12}{0.8192}\approx14.65$ units.

Answer:

A. $m\angle D = 55^{\circ}, DE\approx8.40$ units, $DF\approx14.65$ units