Question

find the perimeter of this triangle.
perimeter = ?
round to the nearest tenth

Explanation:

Step1: Identify known values

Right triangle: $\text{adjacent}=11$, $\theta=50^\circ$

Step2: Find opposite side

Use tangent: $\tan(50^\circ)=\frac{\text{opposite}}{11}$
$\text{opposite}=11\times\tan(50^\circ)\approx11\times1.1918=13.11$

Step3: Find hypotenuse

Use cosine: $\cos(50^\circ)=\frac{11}{\text{hypotenuse}}$
$\text{hypotenuse}=\frac{11}{\cos(50^\circ)}\approx\frac{11}{0.6428}=17.11$

Step4: Calculate perimeter

Sum all sides: $11 + 13.11 + 17.11 = 41.22$

Step5: Round to nearest tenth

$41.22\approx41.3$

Answer:

41.3