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# Consider triangles ABC and DEF such that AB=DE=4 and AC=DF=5, as shown in the picture below:

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Consider triangles ABC and DEF such that AB=DE=4 and AC=DF=5, as shown in the picture below:

If angle a is 30deg, and angle d is arccos(3/5), what are the areas of triangles ABC and DEF, in that order?

Apr 13, 2022

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What are the areas of triangles ABC and DEF, in that order?

Hello Guest!

$$a=30^\circ\\ h_1=5\cdot sin\ 30^\circ=2.5\\ \color{blue}A_{ABC}=\dfrac{4\cdot h_1}{2}=\dfrac{4\cdot 2.5}{2}=5$$

$$d=arccos\ 0.6\\ h_2=5\cdot sin\ arccos\ 0.6=4\\ \color{blue}A_{DEF}=\dfrac{4\cdot h_2}{2}=\dfrac{4\cdot 4}{2}=8$$

!

Apr 13, 2022
edited by asinus  Apr 13, 2022