Triangle tangent area

The tangent of the angle formed by the adjacent sides of the triangle ABC (side a=29 m, b = 40 m) equals 1.05. Calculate the area of that triangle.

Final Answer:

S =  420 m²

Step-by-step explanation:

$$\begin{gathered} a=29\text{m} \\ b=40\text{m} \\ t=1.05 \\ t=\tan \gamma \\ \gamma =\arctan t=\arctan 1.05\doteq 0.8098\text{rad} \\ S=\frac{a\cdot b\cdot \sin \gamma }{2}=\frac{29\cdot 40\cdot \sin 0.8098}{2}=420{\text{m}}^2 \end{gathered}$$

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