These problems can be particularly tricky, especially because there are three similar right triangles and two of the three lie inside the larger one. Exercise #3: In the diagram shown, altitude RU has been drawn to hypotenuse S7 from right angle R. (a) Draw the two smaller triangles in the same orientation as ARST R (b) If RU =10 and TU =5, then find the length of US

These problems can be particularly tricky, especially because there are three similar right triangles and two of the three lie inside the larger one. Exercise #3: In the diagram shown, altitude RU has been drawn to hypotenuse S7 from right angle R. (a) Draw the two smaller triangles in the same orientation as ARST R (b) If RU =10 and TU =5, then find the length of US

Name: These problems can be particularly tricky, especiallybecause there ar
Uploaded: 2024-03-20T06:47:08.000Z
Channel: Bartleby
Description: These problems can be particularly tricky, especiallybecause there are three similar right triangles and twoof the three lie inside the larger one.Exercise #3: In the diagram shown, altitude RU hasbeen drawn to hypotenuse ST from right angle R.(a)Dr

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter5: Similar Triangles

Section5.3: Proving Triangles Similar

Problem 41E: Prove that the altitude drawn to the hypotenuse of a right triangle separates the right triangle...

See similar textbooks

Similar questions

Prove that the altitude drawn to the hypotenuse of a right triangle separates the right triangle into two right triangles that are similar to each other and to the original right triangle.
The diagram shown in Figure 1 was used by the Hindu mathematician Bhaskara to prove the theorem in the 12th century. His proof consisted only of the diagram and the word Behold! Use this figure to derive the Pythagorean Theorem. The right triangle with sides a, b, and c has been repeated three times. The area of the large square is equal to the sum of the areas of the four triangles and the area of the small square in the center. The key to this derivation is in finding the length of a side of the small square. Once you have the equation, simplify the right side to obtain the theorem. Figure 1
Laying Phone Cable City A lies on the north bank of a river that is 1 mile wide. You need to run a phone cable from City A to City B, which lies on the opposite bank 5 miles down the river. You will lay L miles of the cable along the north shore of the river, and from the end of that stretch of cable you will lay W miles of cable running under water directly toward City B. See Figure 2.108. Figure 2.108 You will need the following fact about right triangles: A right triangle has two legs, which meet at the right angle, and the hypotenuse, which is the longest side. An ancient and beautiful formula, the Pythagorean theorem, relates the lengths of the three sides: Lengthofhypotenuse=Lengthofoneleg2+Lengthofotherleg2 a. Find an appropriate right triangle that shows that W=1+(5L)2 b. Find a formula for the length of the total phone cable P from City A to City B as a function of L. c. Make a graph of the total phone cable length P as a function of L, and explain what the graph is showing. d. What value of L gives the least length for the total phone cable? Draw a picture showing the least-length total phone cable.
For the 30-60-90 triangle shown, suppose that XY=2a. Find: a XZ b YZ
In each of the following problems, refer to the given figure, solve for the unknowns, and check. Find the distances between the indicated holes. All dimensions are in millimeters. a. Hole 1 to hole 2 b. Hole 2 to hole 3 C. Hole 3 to hole 4 d. Hole 4 to hole 5 e. Hole 5 to hole 6 f. Hole 2 to hole 4 g. Hole 3 to hole 6