Right angle

In a right triangle ABC with a right angle at the apex C, we know the side length AB = 24 cm and the angle at the vertex B = 71°. Calculate the length of the legs of the triangle.

Correct answer:

a =  7.8136 cm
b =  22.6924 cm

Step-by-step explanation:

$$\begin{gathered} c=24\text{ cm } \\ B=71\text{ ° } \\ \cos B=a:c \\ a=c\cdot \cos B\mathrm{°}=c\cdot \cos 71\mathrm{°}=24\cdot \cos 71\mathrm{°}=24\cdot 0.325568=7.814=7.8136\text{ cm} \end{gathered}$$

$$\begin{gathered} \sin B=b:c \\ b=c\cdot \sin B\mathrm{°}=c\cdot \sin 71\mathrm{°}=24\cdot \sin 71\mathrm{°}=24\cdot 0.945519=22.692=22.6924\text{ cm} \end{gathered}$$

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