Question

solve the right triangle.
write your answers as integers or as decimals rounded to the nearest tenth.
ce =
cd =
m∠e = □°

Explanation:

Step1: Find $m\angle E$

The sum of angles in a triangle is $180^\circ$. For right triangle $\triangle CDE$, $\angle C=90^\circ$, $\angle D=26^\circ$.
$$m\angle E = 180^\circ - 90^\circ - 26^\circ = 64^\circ$$

Step2: Calculate length $CE$

Use sine of $\angle D$: $\sin(D)=\frac{CE}{DE}$. $DE=9$, $\angle D=26^\circ$.
$$CE = 9\times\sin(26^\circ) \approx 9\times0.4384 \approx 4.1$$

Step3: Calculate length $CD$

Use cosine of $\angle D$: $\cos(D)=\frac{CD}{DE}$. $DE=9$, $\angle D=26^\circ$.
$$CD = 9\times\cos(26^\circ) \approx 9\times0.8988 \approx 8.1$$

Answer:

$CE = 4.1$, $CD = 8.1$, $m\angle E = 64^\circ$