📐 geometry

1. **State the problem:** We need to find the area of a right triangle with a base of 17 m and an angle opposite to the base of 22º. 2. **Formula for the area of a triangle:** The

1. **State the problem:** We need to find the area of a right triangle with a base of 89 m and an angle adjacent to the base of 26º. 2. **Formula for the area of a triangle:** The

1. Problem (a): Find the number of planes of symmetry of the cuboid with edges AB = 8 cm, BC = 4 cm, and CR = 5 cm. 2. Explanation: A cuboid has planes of symmetry that divide it i

1. **State the problem:** We are given two angles formed by a transversal intersecting two parallel lines. The angles are \( (15x + 8)^\circ \) and \( (9x + 26)^\circ \). We need t

1. **Problem Statement:** Calculate the angle between line segment $AP$ and the rectangular base $ABCD$ of the triangular prism. 2. **Given Data:**

1. **State the problem:** We are given two parallel lines EF and CD cut by a transversal AB. Angle G is $(85 - 2x)^\circ$ and angle H is $(93 - 4x)^\circ$. Both angles are on the s

1. **State the problem:** We have a right triangle with a base of length 9 and a hypotenuse of length $10 \times \text{pipe size}$. There is an angle of 48 degrees inside the trian

1. **State the problem:** We have a right triangle with legs 9 and $10 \times \text{pipe size}$. We need to find the length TO, which is likely the hypotenuse of this right triangl

1. **Problem statement:** We have a square PQRS with points labeled clockwise: P (bottom-left), Q (top-left), R (top-right), S (bottom-right). Diagonals PR and QS intersect at U (c

1. **Stating the problem:** We need to find the total area of a composite shape consisting of a rectangle and a semicircle attached on the left side of the rectangle.

1. **Problem statement:** We have a square PQRS with points P, Q, R, S in order. Point T lies on side SR such that ST = SR, and point U is inside the square. Given angles are \(\an

1. The problem asks to find the length of segment AB given that segment AD is 13 cm. 2. To solve this, we need more information about the relationship between AB and AD, such as wh

1. The problem seems to involve points lying on the same line within a parallelogram. 2. In a parallelogram, opposite sides are parallel and equal in length.

1. The problem asks for the length of line segment AB. 2. To find the length of a line segment between two points $A(x_1, y_1)$ and $B(x_2, y_2)$ in the coordinate plane, we use th

1. **Stating the problem:** We have a parallelogram ABCD with sides given as $AB = (3x - 5)$ cm, $BC = (2y - 7)$ cm, and $AD = (y + 3)$ cm. We need to analyze the relationships bet

1. **Problem Statement:** We have a square PQRS and point x is the midpoint of side PQ. We need to find the measure of angle $\angle ZPX$ in degrees. 2. **Understanding the problem

1. **Problem 1:** Calculate the length of the minor arc AB of a circle with radius 60 m and central angle 150°. 2. **Formula:** The length of an arc $s$ is given by $$s = r \theta$

1. **Problem statement:** We need to find the length of the arc AB of a sector OAB of a circle where the radius $r = 47$ mm and the central angle $\theta = 66^\circ$. 2. **Formula

1. **Problem statement:** We need to find the length of the minor arc AB of a circle with circumference 95 cm and central angle 72°. 2. **Formula:** The length of an arc $L$ is giv

1. **State the problem:** We are given the surface area of a sphere as $196\pi$ cm$^2$ and need to find the radius $r$ of the sphere. 2. **Formula:** The surface area $A$ of a sphe

1. **State the problem:** We need to find the total surface area of a cone with radius $r=4$ cm and slant height $l=5$ cm, expressed in terms of $\pi$. 2. **Recall the formulas:**