<h3>
Answer: 80 meters</h3>
This is an isosceles triangle. The dashed line is the height which is perpendicular to the base 120. The height is always perpendicular to the base. The dashed line cuts the base into two equal pieces (this only works for isosceles triangles when you cut at the vertex like this).
So we have two smaller triangles each with a base of 60 and a height of x. Focus on one of the right triangles and use the pythagorean theorem to solve for x.
a^2 + b^2 = c^2
x^2 + (60)^2 = (100)^2
x^2 + 3600 = 10000
x^2 = 10000 - 3600
x^2 = 6400
x = sqrt(6400)
x = 80
Each smaller right triangle has side lengths of 60, 80, 100
Note the ratio 60:80:100 reduces to 3:4:5. A 3-4-5 right triangle is a very common pythagorean primitive.
Answer:
5.44 cm³
Step-by-step explanation:
The volume of the hexagonal nut can be found by multiplying the area of the end face by the length of the nut. The end face area is the difference between the area of the hexagon and the area of the hole.
The area of a hexagon with side length s is given by ...
A = (3/2)√3·s²
For s=1 cm, the area is ...
A = (3/2)√3(1 cm)² = (3/2)√3 cm²
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The area of a circle is given by ...
A = πr²
The radius of a circle with diameter 1 cm is 0.5 cm. Then the area of the hole is ...
A = π(0.5 cm)² = 0.25π cm²
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The volume is the face area multiplied by the length, so is ...
V = Bh = ((3/2)√3 -0.25π)(3) . . . . . cm³
V = (9/2)√3 -0.75π cm³ ≈ 5.44 cm³
The volume of the metal is about 5.44 cm³.
Step-by-step explanation:
the answer is in the image above
Answer and Step-by-step explanation:
90ft = a
55ft = b
50ft = c
Plug into equation.
29.4° is the answer.
Answer:
x = 5
Step-by-step explanation:
