two right triangles share a common side and have equal areas. the hypotenuse of the light green triangle is one of the legs of dark green triangle stacked on top of it. if the smallest angle of light green triangle is 18 degrees, what are the angles of the dark green triangle?

Question

Mathematics

Franco Meyer

23 October, 04:50

two right triangles share a common side and have equal areas. the hypotenuse of the light green triangle is one of the legs of dark green triangle stacked on top of it. if the smallest angle of light green triangle is 18 degrees, what are the angles of the dark green triangle?

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Answers (1)

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Honey Locks · Answer 1

the two angles of dark green triangle are 90 degrees, 72 degrees and 18 degrees.

Step-by-step explanation:

As dark green triangle is stacked on top of light green triangle and one side of dark green is sharing hypotenuse of light green, considering both have same area, mean same 1/2 base * height, also one leg of both is same so its obvious that both heights and bases of triangles are same. Considering all the above facts both triangles are forming a square with common side as diagonal of square.

So, the angles of light green triangle are 90, 18 and (180-90-18) = 72 degrees

One angle of dark green is already 90 degrees, the other two combined with light green form 90 degrees (as both are side angles of square).

90-18=72

90-72=18

Hence the three angles of dark green triangle are 90,72 and 18.