📐 geometry

1. **Problem:** Find the value of side AB in a right triangle with vertices A, B, C, where angle B is 90°, AC = 12, and angle C = 62°. 2. **Formula:** Use the sine function in a ri

1. **Problem:** Work out the bearings of P from Q for diagram (a). 2. **Understanding bearings:** Bearings are measured clockwise from the North direction.

1. Το πρόβλημα ζητά να κατανοήσουμε την έννοια της ευθείας στη μαθηματική ενότητα της ευθείας. 2. Μια ευθεία είναι το απλούστερο γεωμετρικό αντικείμενο που εκτείνεται απεριόριστα π

1. **State the problem:** We are given two intersecting lines forming four angles labeled 1, 2, 3, and 4. We know that $m\angle 2 = 126^\circ$. We need to find $m\angle 1$, $m\angl

1. **State the problem:** We need to find the size of angle $x$ in triangle $BEG$ given that lines $ABC$ and $DEF$ are parallel and several angles are provided. 2. **Identify known

1. **State the problem:** Macsen's garden has a right triangle with base 14 m and height 16 m, and an inscribed circle with diameter 7 m. We need to find how many bags of gravel ar

1. **State the problem:** Find the perimeter of a composite figure made of a rectangle and a semicircle attached on one side. 2. **Given dimensions:** Rectangle height = 6 m, width

1. The problem states that a map is drawn to a scale of 1 cm to 10 km. 2. We need to express this scale in the form 1 : n, where both units are the same.

1. **Stating the problem:** We have a triangle inscribed in a circle with one angle inside the triangle labeled $45^\circ$, an exterior angle near the chord labeled $88^\circ$, and

1. **State the problem:** We have two intersecting chords inside a circle creating four angles. One angle is 137°, the angle opposite it is $x$, and another angle adjacent to $x$ i

1. **State the problem:** We have two intersecting lines forming four angles. One angle is 59° and we need to find the measures of angles $x$ and $y$. 2. **Recall important rules:*

1. **Problem statement:** Given an acute triangle $\Delta ABC$ with $AB < AC$ inscribed in circle $(O; R)$. Altitudes $BK$ and $CH$ are drawn. The bisector of angle $\widehat{BAC}$

1. **State the problem:** We need to determine if Olio will need more wire than Ellie to install around their painting and its border.

1. **State the problem:** We need to find the volume of a pentagonal prism where each side of the pentagonal base is 8 inches and the height of the prism is 5.5 inches. 2. **Formul

1. **State the problem:** We need to find the volume of a hexagonal prism with side length $4$ ft, height $3$ ft, and apothem $3.5$ ft. 2. **Formula for volume of a prism:**

1. **State the problem:** Find the volume of a cylinder with height $7$ km and radius $8$ km. 2. **Formula for volume of a cylinder:**

1. **Problem statement:** Find the angles $x$ and $y$ in the first figure where two parallel lines are intersected by a transversal, forming angles $72^\circ$, $y$, $x$, and $60^\c

1. **Problem statement:** Determine the perimeter of the right triangle with sides DE = 8.8 cm, hypotenuse DC = 10.6 cm, and angle ∠E = 34°. 2. **Formula and rules:** The perimeter

1. **State the problem:** We need to find the bearing from point O to point A. 2. **Understanding bearings:** Bearings are measured clockwise from the North direction.

1. **State the problem:** We need to find the bearing from point O to point A. 2. **Understanding bearings:** Bearings are measured clockwise from the north direction. The angle gi

1. **State the problem:** We have two similar right triangles. The smaller triangle has legs 3 m and 5 m, and the larger triangle has a base of 50 m and an unknown height (the heig