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:

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

$$\begin{gathered} K+L+M=180^{\circ } \\ K=180-L-M=180-90-65=25^{\circ } \end{gathered}$$

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

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