📐 geometry

1. **State the problem:** We have triangle ABC with sides $AB = 15$ cm, $AC = 25$ cm, angle $BAC = \theta^\circ$, and area $= 100$ cm². We need to find (a) $\sin \theta$ and (b) th

1. **State the problem:** We need to find the volume of a cone-shaped mold with radius $r=0.5$ meters and height $h=1.8$ meters. 2. **Formula for the volume of a cone:**

1. **State the problem:** We need to find the area of a triangle given its vertices on a coordinate grid. 2. **Identify the vertices:** From the description, the triangle's vertice

1. **Problem statement:** We have a construction made of black and white rods where all black rods are equal in length and all white rods are equal in length. An angle of 40° is gi

1. **State the problem:** We have a construction with black rods all equal in length and white rods all equal in length. An angle of $40^\circ$ is given, and we need to find the an

1. **Find the size of the unknown angle in each question and state the property used:** a) Given angle is $130^\circ$ and adjacent angle $a$ forms a straight line.

1. **State the problem:** We need to find the new coordinates of point $J'(-5, -1)$ after applying the translation rule $ (x, y) \to (x - 2, y) $. 2. **Understand the translation:*

1. **State the problem:** We need to find the new coordinates of point $M(-1, 5)$ after applying the translation rule $(x, y) \to (x + 3, y - 2)$. 2. **Recall the translation formu

1. **State the problem:** We need to find the new coordinates of point $R(2, 1)$ after applying the translation rule $(x, y) \to (x, y - 5)$. 2. **Understand the translation:** The

1. **State the problem:** We need to find the new coordinates of point $G(-3, 9)$ after applying the translation rule $(x, y) \to (x + 10, y - 7)$. 2. **Recall the translation form

1. **State the problem:** We need to find the new coordinates of point $M(-3, -4)$ after applying the translation rule $(x, y) \to (x + 4, y)$. 2. **Recall the translation formula:

1. **State the problem:** We need to find the new coordinates of point $Z(-3, 1)$ after applying the translation rule $(x, y) \to (x - 2, y - 7)$. 2. **Recall the translation formu

1. **Problem Statement:** Reflect each given figure across the specified reflection line. 2. **Reflection Rules:**

1. **Nyatakan masalah:** (a) Garis lurus ACB adalah tangen kepada bulatan di titik C. Segi tiga CDE adalah sama kaki. Cari nilai $x + y + z$.

1. **State the problem:** Find the equation of a circle passing through the intersection points of two given circles and tangent to a given line.

1. **State the problem:** We need to find the length of side $b = AC$ in triangle $BAC$ where $BA = 14$ cm, $BC = 77$ cm, and angle $B = 34^\circ$. 2. **Identify the formula:** Use

1. Vấn đề: Người dùng yêu cầu vẽ hình, tuy nhiên không có thông tin cụ thể về hình dạng hoặc các kích thước liên quan. 2. Vì không có dữ liệu cụ thể, không thể tạo ra một hình vẽ c

1. **Nêu bài toán:** Cho góc $xOy$, điểm $A$ thuộc tia $Ox$. Kẻ các đoạn thẳng $AB$, $BC$, $CD$ sao cho $AB$ vuông góc với $Ox$ tại $B$ thuộc tia $Oy$, $BC$ vuông góc với $Oy$ tại

1. Let's start by understanding what an angle is. An angle is formed by two rays (or line segments) that share a common endpoint called the vertex. 2. The measure of an angle is us

1. **Problem Statement:** Calculate the area of the given quadrilateral-like shape with sides 4 cm, 4 cm, and an angle of 75° between them, where a segment from the top point to th

1. **Problem statement:** We have a figure with two sides of length $4$ cm each and an angle of $75^\circ$ at the top vertex. We want to find the length $h$ (likely the height or a