Triangle XYZ is rotated 90° counterclockwise using the origin as the center of rotation.
2 answers:
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Check the picture below.
the triangle is an isosceles, so it has twin legs, and a base bottom.
the twin sides stem from the "vertex", and we know the vertex is 120°, and since the triangle is inscribed in a circle, because the circle is "circumscribing" it, then the base side of the triangle will be the diameter of it.
if we run a perpendicular line to the base from the vertex, we'll split the vertex in two 60° angles, as you see there, giving us a 30-60-90 triangle on each side.
so, anyhow, the rest is just a matter of using the 30-60-90 rule.
that's the diameter, and as you know, the radius is just the length of the base, or half the diameter.
the triangle is an isosceles, so it has twin legs, and a base bottom.
the twin sides stem from the "vertex", and we know the vertex is 120°, and since the triangle is inscribed in a circle, because the circle is "circumscribing" it, then the base side of the triangle will be the diameter of it.
if we run a perpendicular line to the base from the vertex, we'll split the vertex in two 60° angles, as you see there, giving us a 30-60-90 triangle on each side.
so, anyhow, the rest is just a matter of using the 30-60-90 rule.
that's the diameter, and as you know, the radius is just the length of the base, or half the diameter.
Answer:
Q7. 11.3 inches (3 s.f.)
Q8. 96.2 ft
Q9. 36.4cm
Step-by-step explanation:
Q7. Please see attached picture for full solution.
Q8. Let the length of a side of the square be x ft.
Applying Pythagoras' Theorem,
Thus, the perimeter of the square is
Q9. Equilateral triangles have 3 equal sides and each interior angle is 60°.
Since the perimeter of the equilateral triangle is 126cm,
length of each side= 126÷3 = 42 cm
The green line drawn in picture 3 is the altitude of the triangle.
Let the altitude of the triangle be x cm.
sin 60°=
(to 3 s.f.)
Therefore, the length of the altitude of the triangle is 36.4cm.
