You randomly draw twice from this deck of cards
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According to given conditions, m+n is equal to 409.
Consider the diagram below.
In the hexagon ABCDEF, let
AB = BC = CD = 3;
DE = EF = FA = 5;
Arc BAF is equal to one-third of the circle's circumference.
Hence, ∠BCF = ∠BEF = 60°;
Similarly, ∠CBE = ∠CFE = 60°;
Let the point of intersection of BE and CF be P, BE and AD be Q and CF and AD be R.
∴ Δ EFP and Δ BCP are equilateral, and so Δ PQR is also equilateral.
Also, ∠ BAD and ∠ BED subtend the same arc and so do ∠ ABE and ∠ ADE.
∴ Δ ABQ is similar to Δ EDQ
Also,
and
On solving these simultaneous equations, we get AD = 360/49
∴ m + n = 409.
To learn more about similarity of triangles, refer to this link:
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Answer:
Step-by-step explanation:
For a triangle the area is
If our triangle is isosceles and the 2 congruent sides each measure 4 and they include an angle of 40 degrees, let's say that the vertex angle is 40 and the sides that are not the base each measure 4. If we drop an altitude from the vertex to the base, we cut the triangle into 2 right triangles, with the vertex angle being 20 degrees and the hypotenuse being 4. To find the base, then, which is opposite the angle, we use the sin ratio:
and
4sin(20) = b so
b = 1.368
But we need the whole base, and that is only half of it. So
2b = 2.736
To find the height, which is adjacent to the angle, we use the cos ratio:
and
4cos(20) = h so
h = 3.759
Now we have enough info to find the area of the triangle using the triangle area formula from above:
and
A = 5 meters squared.