Rectangular

Rectangular triangle KLM with right angle at vertex L, angle beta at vertex K and angle alpha at vertex M. Angle at vertex M = 65°, side l = 17.5 cm. Use Pythagorean theorems and trigonometric functions to calculate the lengths of all sides and the angle at the vertex K.

Correct answer:

m =  15.8604 cm
K =  25 °
k =  7.3958 cm

Step-by-step explanation:

$$\begin{gathered} L=90\text{ ° } \\ M=65\text{ ° } \\ l=17.5\text{ cm } \\ \sin M=m:l \\ m=l\cdot \sin M\mathrm{°}=l\cdot \sin 65\mathrm{°}=17.5\cdot \sin 65\mathrm{°}=17.5\cdot 0.906308=15.86=15.8604\text{ cm} \end{gathered}$$

$$\begin{gathered} K+L+M=180\mathrm{°} \\ K=180-L-M=180-90-65=25\text{°} \end{gathered}$$

$$\begin{gathered} \sin K=k:l \\ k=l\cdot \sin K\mathrm{°}=l\cdot \sin 25\mathrm{°}=17.5\cdot \sin 25\mathrm{°}=17.5\cdot 0.422618=7.396=7.3958\text{ cm} \end{gathered}$$

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