📐 geometry

1. **Problem statement:** We have a right triangle ABC with vertical side AB = 2 m, horizontal side BC = 3 m, and hypotenuse AC. We need to find:

1. **State the problem:** We need to find the total surface area of a cylinder given its net. 2. **Identify the parts of the net:** The net consists of a rectangle and two circles.

1. **State the problem:** We are given a cylinder with a top face area of $14\pi$ cm² and a curved surface area of $29\pi$ cm². We need to find the total surface area of the cylind

1. **State the problem:** We have a circle with center $O$ and two chords inside it. We need to find the lengths $a$ and $b$ of parts of these chords.

1. **State the problem:** We have a right triangle with a hypotenuse of length 29 inches and a vertical side (height) of 14 inches. We need to find the length of the horizontal sid

1. **State the problem:** We need to find the coordinates of the centre of enlargement that maps shape A onto shape B. 2. **Understanding centre of enlargement:** The centre of enl

1. **State the problem:** We are given two intersecting lines forming four angles. One angle is 89° at the top, and at the bottom right, there is an angle of 22° adjacent to angle

1. Planteamos el problema: Tenemos una valla que actúa como hipotenusa de un triángulo rectángulo con longitud $\sqrt{200}$ metros. Queremos encontrar las medidas de los otros dos

1. **State the problem:** We need to find the angle $c$ in a triangle or geometric figure. 2. **Identify the known information:** Since the problem is brief, we assume we have a tr

1. **State the problem:** We need to find the size of angle $c$ in a triangle where two sides are equal, and two angles are given as $30^\circ$ and $51^\circ$. 2. **Recall the prop

1. **State the problem:** We are given the line equation $y = -\frac{4}{3}x + 4$ and need to:

1. **Stating the problem:** We have two parallel lines \(\overline{HE}\) and \(\overline{AD}\) intersected by a transversal \(\overline{BF}\) at points \(G\) and \(C\). Given \(m\a

1. **State the problem:** We have two satellites orbiting Earth. The first satellite's orbit is a circle with equation $x^2 + y^2 = 56250000$. The second satellite's orbit is 200 k

1. **State the problem:** We need to find the area of a square room with side length $2 \frac{1}{5}$ meters. 2. **Formula:** The area $A$ of a square is given by:

1. **State the problem:** We are given a triangle with sides and an angle, and the equation $$x^2 = 8.3^2 + c^2 - 2(8.3)(c) \cos 61^\circ$$ which comes from the cosine rule. We nee

1. **Problem Statement:** Given triangle $ABC$ with $\overline{AB} \cong \overline{AC}$ (isosceles triangle), and $AD$ bisects $\angle BAC$. We need to prove that $$\frac{BD}{AD} \

1. **Problem statement:** Calculate angle $\phi$ in degrees and minutes. 2. **Understanding the problem:** Angle $\phi$ is part of the polygon's interior angles. We need to find it

1. **Problem statement:** Determine the length of chord $PQ$ in the circle with center $C$, where $CP = CQ = 18$ m and the angle $\angle RPQ = 15^\circ$. The segment $RP = 35$ m.

1. **State the problem:** We have a triangle DEF with angles labeled as follows: angle E is 64°, angle D is 2x, and there is an adjacent angle of 42° at vertex F on the line DG. We

1. **Problem Statement for Q2:** Find the values of angles $a$ and $b$ given that they are adjacent to a 135° angle and form a right angle (small square) between them.

1. **Problem statement:** We need to show that the area $A$ of an equilateral triangle with side length $s$ is given by $$A = \frac{1}{4}s^2\sqrt{3}.$$\n\n2. **Recall the formula f