Question

q.13 solve a right triangle. gpr
solve the right triangle.
write your answers as integers or as decimals rounded to the nearest tenth.
$ce = $
$de = $
$m\angle e = \quad ^\circ$
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work it out
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Explanation:

Step1: Find $m\angle E$

Sum of angles in triangle: $180^\circ - 90^\circ - 41^\circ = 49^\circ$

Step2: Calculate hypotenuse $CE$

Use $\cos C = \frac{DC}{CE}$, so $CE = \frac{DC}{\cos 41^\circ} = \frac{6.8}{\cos 41^\circ} \approx 9.0$

Step3: Calculate leg $DE$

Use $\tan C = \frac{DE}{DC}$, so $DE = DC \cdot \tan 41^\circ = 6.8 \cdot \tan 41^\circ \approx 5.9$

Answer:

$CE = 9.0$
$DE = 5.9$
$m\angle E = 49^\circ$