📐 geometry

1. **State the problem:** We need to find the bearing of point B from point A using the given semicircle protractor. 2. **Understanding bearings:** Bearings are measured clockwise

1. **Problem statement:** We need to find the length of the fence BD and the area of the quadrilateral ABCD with given sides and angles. 2. **Given data:**

1. **Problem Statement:** We have a quadrilateral ABCD with sides AB = 246 m, BC = 312 m, AD = 257 m, and angles \(\angle DÂB = 96^\circ\) and \(\angle BĈD = 78^\circ\). We need to

1. **Problem 1(a):** Calculate $x$ in a right triangle with legs 4 cm and 6 cm, hypotenuse $x$. 2. Use the Pythagorean theorem formula: $$x^2 = a^2 + b^2$$ where $a$ and $b$ are le

1. **State the problem:** We need to find the measure of angle $g$ in a figure composed of a regular octagon, a regular hexagon, a square, and an equilateral triangle. 2. **Recall

1. **Problem statement:** Given an acute triangle $ABC$ with $AB < AC$, and a variable point $P$ on side $BC$. Define $\omega_B$ as the circle passing through $P$ and tangent to $A

1. **State the problem:** We are given triangle ABC with a right angle at E inside it. AE = BE, AC = 12, and DC = 5. We need to find the area of triangle BED. 2. **Identify known l

1. 問題陳述：已知△ABC 和 △A₁B₁C₁ 是以點 O 為位似中心的位似三角形，且 C₁ 是 OC 的中點，△ABC 的周長為 4，求 △A₁B₁C₁ 的周長。 2. 位似三角形的周長比例與位似比相同。若位似中心為 O，且 C₁ 是 OC 的中點，表示位似比為 $\frac{1}{2}$。

1. **Stating the problem:** We are given a rectangular prism with dimensions $a=14$, $b=8$, and an unknown $c$. The volume $V=2912$ cm³ is given, and we want to find the surface ar

1. **Stating the problem:** We are given points A(-2,3), B(4,-5), C(-3,-4), D(0,5), and E(6,0) plotted on a coordinate plane. 2. **Understanding the task:** Since no specific quest

1. **State the problem:** Calculate the area of the triangle with vertices at points $A(1,2)$, $B(9,2)$, and $C(6,7)$. 2. **Formula for the area of a triangle:** The area $A$ of a

1. **State the problem:** We have a cone with base diameter 20 cm and slant height 25 cm. A circle is drawn on the cone's surface at 10 cm above the base along the slant height. We

1. **State the problem:** We need to find the measure of angle $\angle AB$ in triangle $ABC$ with a right angle at $D$ and given angles $71^\circ$ at $A$ and $71^\circ$ at $C$. 2.

1. **State the problem:** We have triangle PQRS with a segment QT parallel to RS. Given QT = 2x, PR = 15, TS = 12, and RS = x + 26, we want to find the value of $x$ using the prope

1. **State the problem:** Find the angle between the line AG and the plane ABCD in the cuboid with edges 15.3 cm, 9.5 cm, and 8.3 cm. 2. **Identify the dimensions and points:**

1. The problem asks to identify the term that best describes points W, X, Y, and Z in the given 3D figure. 2. Definitions:

1. **State the problem:** Determine which sets of points among the given options are collinear, meaning they lie on the same straight line. 2. **Given information:** Points B, Q, a

1. **Problem statement:** Calculate the total surface area of a solid cylinder with radius $3$ m and volume $72\pi$ m³. 2. **Given:**

1. **State the problem:** A man whose eyes are 6 ft above the ground sees the top of a pole and the top of a building aligned in a straight line of sight. The pole is 10 ft away an

1. **State the problem:** A girl 160 cm tall stands 360 cm from a lamp post. Her shadow is 90 cm long. We need to find the height of the lamp post. 2. **Use the concept of similar

1. **Stating the problem:** We have a tetrahedron with a triangular base. The base triangle has sides 7 cm and 5 cm, and the height from the base to the apex (top vertex) is 13 cm.