What is a1? what is d? what’s the equation? what is a7? what is a59?
2 answers:
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Answer:
A ≈ 40.3 cm²
Step-by-step explanation:
The area of right Δ ACD is calculated as
A = bh ( b is the base and h the perpendicular height )
Here A = 50.5, b = CD and h = AC , then
× 14 × AC = 50.5
7 AC = 50.5 ( divide both sides by 7 )
AC ≈ 7.214
The area of Δ ABC is calculated as
A = × BC × AC × sin36°
= 0.5 × 19 × 7.214 × sin36°
≈ 40.3 cm² ( to 3 sf )
The picture in the attached figure
we know that
the area of the shaded region is equal to
(2/3)*[area of the circle - the area of the triangle]
step 1
Find the area of a circle Ac
Ac = π r²
Ac = π (6)²
Ac = 113.10 units²
step 2
find the area of the triangle At
The triangle is an equilateral triangle with angles on each corner equal to 60 degrees. Meanwhile,
the 3 angles at the center is 120 degrees each since a circle is 360 degree.
We know that the radius (line from centerpoint to corner) is equivalent to 6.
Using the cosine law,
we can calculate for the length of one side.
s² = 6^ + 6² – 2 (6) (6) cos 120
s² = 108
s = 10.4 units
Since this is an equilateral triangle, therefore, all sides are equal.
The area for this is:
At = (sqrt3 / 4) * s²
At = 46.77 units²
step 3
the area of the shaded region=(2/3)*[area of the circle - the area of the triangle]
the area of the shaded region=(2/3)*[113.10-46.77]------> 44.22 units²
therefore
the answer is
the area of the shaded region is 44.22 units²
we know that
the area of the shaded region is equal to
(2/3)*[area of the circle - the area of the triangle]
step 1
Find the area of a circle Ac
Ac = π r²
Ac = π (6)²
Ac = 113.10 units²
step 2
find the area of the triangle At
The triangle is an equilateral triangle with angles on each corner equal to 60 degrees. Meanwhile,
the 3 angles at the center is 120 degrees each since a circle is 360 degree.
We know that the radius (line from centerpoint to corner) is equivalent to 6.
Using the cosine law,
we can calculate for the length of one side.
s² = 6^ + 6² – 2 (6) (6) cos 120
s² = 108
s = 10.4 units
Since this is an equilateral triangle, therefore, all sides are equal.
The area for this is:
At = (sqrt3 / 4) * s²
At = 46.77 units²
step 3
the area of the shaded region=(2/3)*[area of the circle - the area of the triangle]
the area of the shaded region=(2/3)*[113.10-46.77]------> 44.22 units²
therefore
the answer is
the area of the shaded region is 44.22 units²
Answer:
3 metres
Step-by-step explanation:
If we draw this out, we'll see that there are actually two similar right triangles (see attachment), which means that we can set up a proportion.
The height of the lookout tower corresponds to the height of the wooden column, while the shadow of the lookout tower corresponds to the shadow of the wooden column. We can then write:
(height of lookout tower) / (shadow of tower) = (height of column) / (shadow of column)
16 / 12 = 4 / x , where x is the shadow / unknown we want to find
Cross-multiply:
16x = 48
x = 3
The answer is thus 3 metres.
