📐 geometry

1. **State the problem:** We have a right triangle IHG with a right angle at H. Given: IH = 9.5, GH = 4.1, and we need to find angle $x$ at vertex G.

1. **State the problem:** We have two similar right triangles \(\triangle ABC \sim \triangle YXZ\) with a right angle at \(C\) in \(\triangle ABC\) and at \(Z\) in \(\triangle YXZ\

1. 문제: 사다리꼴의 넓이를 구하시오. 2. 사다리꼴 넓이 공식은 $$\text{넓이} = \frac{(\text{윗변} + \text{밑변}) \times \text{높이}}{2}$$ 입니다.

1. **State the problem:** We have a rectangle CDGH with sides labeled as follows: - Top side DG = $x + 10$

1. **State the problem:** We have a right triangle ABC with a right angle at A. The other two angles are given as $(3x + 9)^\circ$ and $(4x - 3)^\circ$. We need to find the value o

1. The problem asks to write a rule describing the transformation shown in the first graph of a polygon and its image on a coordinate grid. 2. To describe a transformation, we iden

1. **State the problem:** Find the lateral and total surface area of the rectangular prism with base dimensions 10.5 cm by 4 cm and height 8.25 cm. 2. **Formulas:**

1. **Stating the problem:** We need to determine if Missy's method for calculating the amount of plastic wrap needed to cover a triangular prism is correct. The prism has a triangu

1. **State the problem:** Given angles with expressions in terms of $x$, find $m\angle RT$ where $m\angle QT = (27x + 3)^\circ$,

1. **State the problem:** Find the height above the first floor of a shopping mall where a 40-foot-long escalator rises at a 30° angle with the horizontal.

1. **State the problem:** Find the total area of the two composite figures by decomposing each into familiar shapes. ---

1. **State the problem:** We have a semicircle with center O and radius $r$. Points P and Q lie on the horizontal diameter, with P at the right endpoint and O at the center. Point

1. **State the problem:** Calculate the surface area of a cone with height $12$ feet, slant height $15$ feet, and radius $9$ feet.

1. **Problem Statement:** Find the surface area of a cone with radius $r=4$ m, height $h=3$ m, and slant height $l=5$ m. 2. **Formula:** The total surface area $A$ of a cone is giv

1. **State the problem:** We have a right triangle with a hypotenuse of length 10, an angle of 31°, and the side opposite this angle labeled as $x$. We need to find $x$. 2. **Formu

1. **Stwierdzenie problemu:** Mamy trójkąt ABC z podstawą AB podzieloną na AP = 2 i PB = 8, więc AB = 10.

1. **State the problem:** We need to find the area of a compound shape made of a rectangle and a sector of a circle. 2. **Identify given values:**

1. **Problem:** Given points $A=(-3,-1)$ and $B=(2,5)$ are two vertices of an equilateral triangle $ABC$. Find the area of this triangle. 2. **Formula and rules:**

1. **State the problem:** We have a right triangle with legs of lengths 8 meters and 4 meters, and the hypotenuse labeled as $b$. We need to find the length of $b$. 2. **Formula us

1. **State the problem:** We have a right triangle with a hypotenuse of 78 ft and one leg of 72 ft. We need to find the length of the missing leg $a$. 2. **Formula used:** In a rig

1. **State the problem:** We have a right triangle with legs of length $x$ and $x$, and the hypotenuse is $3\sqrt{2}$. We need to find the value of $x$ in simplest form. 2. **Formu