Calculate 83261

Calculate the area of the triangle ABC, in which you know the side c=5 cm, the angle at the top A= 70 degrees, and the ratio of the segments cut by the height to the side c is 1:3

Correct answer:

S =  25.7576 cm²

Step-by-step explanation:

$$\begin{gathered} c=5\text{cm} \\ \alpha =70{}^{\circ } \\ {c}_1:c_2=1:3 \\ {c}_1=\frac{1}{1+3}\cdot c=\frac{1}{1+3}\cdot 5=\frac{5}{4}=1.25\text{cm} \\ {c}_2=c-c_1=5-1.25=\frac{15}{4}=3.75\text{cm} \\ \tan \alpha =h:c_2 \\ h=c_2\cdot \tan \alpha =c_2\cdot \tan 70°=3.75\cdot \tan 70°=3.75\cdot 2.747477=10.30304\text{cm} \\ S=\frac{c\cdot h}{2}=\frac{5\cdot 10.303}{2}=25.7576{\text{cm}}^2 \end{gathered}$$

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