📐 geometry

1. **Problem 15: Find the missing side of a right triangle with sides 12 ft (hypotenuse), 6 ft, and 7.1 ft.** 2. Use the Pythagorean theorem for right triangles: $$a^2 + b^2 = c^2$

1. The problem states that a 10x8 grid is divided vertically into two halves: the left half (5 columns) painted yellow and the right half (5 columns) painted blue. 2. Then, it says

1. **Problem statement:** Given chords intersecting inside a circle, find the unknown length using the chord intersection theorem. 2. **Theorem:** For two chords intersecting insid

1. **Problem Statement:** We analyze the geometric properties of the Ontario flag and design a flag incorporating various angle relationships.

1. **Problem Statement:** Analyze the flag of Ontario focusing on its geometric shapes, angles, and measurements. 2. **Q1a: Number of Different Triangles**

1. **Problem Statement:** We are given a circle centered at point A with points B, C, D, and E on the circumference. Segments BE, BC, CD, and DE are drawn, forming angles at points

1. Problema: Encontrar a equação do plano que passa pelos pontos A(1,0,1), B(0,2,1) e C(0,0,3). 2. Fórmula: A equação do plano pode ser encontrada usando o vetor normal \(\vec{n} =

1. **State the problem:** We need to find the area of the center section of a drop-leaf table when the leaves are down. The center section corresponds to the area of a circular seg

1. **State the problem:** We need to find the area of the center section of a circular table when the drop-leaves are down. The table has a diameter of 44 in., so the radius is 22

1. **Problem 1:** We have two rectangles.

1. **Problem 8:** Given \(\triangle MTW \cong \triangle BGK\), find \(x\) and \(y\) where angles are \(\angle T = (4x - 3)^\circ\), \(\angle G = 45^\circ\), \(\angle B = (11y + 6)^

1. **State the problem:** We need to find the tangent of angle $B$ in a right triangle with sides $AC=16$, $CB=12$, and hypotenuse $AB=20$. 2. **Recall the definition of tangent:**

1. **Problem Statement:** Find the tangent of angle $\angle J$ in the right triangle with sides $KJ=12$, $KI=35$, and hypotenuse $IJ=37$. 2. **Formula:** The tangent of an angle in

1. **Problem Statement:** We are examining the reflexive property in geometry, which states that a segment or angle is equal to itself, often written as $AB = BA$. 2. **Context:**

1. **State the problem:** We have two mathematically similar shapes. The smaller shape has an area of 52.5 cm² and a side length of $m$ cm. The larger shape has an area of 134.4 cm

1. **State the problem:** We have a circle with center O and radius $r$ cm. Points A and B lie on the circumference, and the central angle $\angle AOB$ is 140°. The area of the sha

1. **State the problem:** We are given a trapezium with two angles on the left side: the top-left angle is $97 - 3x$ degrees and the bottom-left angle is $69 + 5x$ degrees. We need

1. **State the problem:** We are given a trapezium with two angles on the left side: the top left angle is $97 - 3x$ degrees and the bottom left angle is $69 + 5x$ degrees. We need

1. The problem asks for the name of a quadrilateral with rotational symmetry of order 2 and no lines of symmetry. 2. Rotational symmetry of order 2 means the shape looks the same a

1. The problem asks to identify quadrilaterals based on their symmetry properties. 2. (a) A quadrilateral with rotational symmetry of order 2 but no lines of symmetry is called a *

1. **Stating the problem:** We need to find the volume of the frustum of a pyramid OABCD, where the height of the frustum is 16 cm, and the base and top areas are related to the gi