The Pythagorean Theorem is a cornerstone of geometric principles, asserting that in a triangle with a right angle, the square of the length of the hypotenuse (the side not connected to the right angle) equals the combined squares of the lengths of the other two sides. This can be summarized by the equation: a² + b² = c².
| Topic | Problem | Solution |
|---|---|---|
| None | The length of a shadow of a building is $26 \math… | This problem can be solved using the Pythagorean theorem, which states that in a right triangle, th… |
| None | For the following right triangle, find the side l… | For the following right triangle, find the side length $x$. Round your answer to the nearest hundre… |
| None | For the following right triangle, find the side l… | By similarity, we know that \(\frac{a}{x} = \frac{b}{c}\), so therefore \(x = \frac{ac}{b}\). |
| None | A surveyor wants to know the length of a tunnel b… | Given that the surveyor is located 212 meters from one entrance of the tunnel, at an angle of \(57^… |
| None | A plane is descending at an angle of $1^{\circ}$ … | Given that the plane is descending at an angle of \(1^{\circ}\) from the horizontal, and the plane'… |
| None | 3. A ladder leans against a house making a 30^ a… | This problem involves a right triangle, where the angle between the ladder and the ground is given,… |
| None | A flagpole has a height of 15 yards. It will be s… | Given a flagpole with a height of 15 yards, it will be supported by three cables. Each cable is att… |
| None | A 13-foot ladder is placed against a vertical wal… | Given a 13-foot ladder is placed against a vertical wall of a building, with the bottom of the ladd… |
| None | Find the height of a pine tree that casts a 86 -f… | First, we need to convert the angle of elevation from degrees and minutes to decimal form. We know … |
| None | Example 9 A vertical mast is supported at the top… | We are given a right triangle with the hypotenuse (the cable from point A) and an angle. We can use… |
| None | 1. Isabelle is flying a kite on a windy day. When… | Let the length of the string be L, the height of the kite be H, and the angle of elevation be A. We… |
| None | CRITICAL THINKING In the figure, $A B=12, B C=8$,… | Let the radius of the circle be \(r\). Since A is a point of tangency, AP is perpendicular to the t… |
| None | In $\triangle \mathrm{OPQ}, q=18 \mathrm{~cm}, o=… | Given: \(o = 96\), \(q = 18\), and \(\angle P = 142^\circ\) |
| None | Aufgabe 3 Berechnen Sie im Dreieck \( A B C \) zu… | \(h_c = \frac{2A}{a}\) |
| None | Übungsaufgaben Aufgabe 1 Überprüfen Sie, ob das D… | \( a^{2} + b^{2} = c^{2} \) |
| None | Ai Mi is 1.45 meters tall. At 11 a.m., she measur… | \( \frac{h}{27.65} = \frac{1.45}{22.8} \) |