Find Length of Side in Right Triangle w/ 45°, 90°, and 45° Angle

  • Context: MHB 
  • Thread starter Thread starter Monoxdifly
  • Start date Start date
  • Tags Tags
    Angle Triangle
Click For Summary
SUMMARY

The discussion focuses on finding the length of side AD in a right triangle ABC, where angle A is the right angle, and angle B is bisected by line BD. Given that AB measures 12 cm and BC measures 15 cm, the Angle Bisector Theorem is applied to derive the length of AD. The equation established is AD/12 = (9 - AD)/15, leading to the conclusion that AD equals 6 cm. This problem illustrates the application of the Angle Bisector Theorem in solving for unknown lengths in right triangles.

PREREQUISITES
  • Understanding of right triangles and their properties
  • Familiarity with the Angle Bisector Theorem
  • Basic algebra for solving equations
  • Knowledge of triangle side length ratios
NEXT STEPS
  • Study the derivation and applications of the Angle Bisector Theorem
  • Learn about the properties of 45°-90°-45° triangles
  • Explore Pythagorean theorem applications in various triangle types
  • Investigate other triangle theorems, such as the Law of Sines and Cosines
USEFUL FOR

Students in geometry, educators teaching triangle properties, and anyone interested in mastering the application of the Angle Bisector Theorem in right triangles.

Monoxdifly
MHB
Messages
288
Reaction score
0
The triangle ABC is a right triangle with A as the right angle and BD is the bisector of angle B. If AB = 12 cm and BC = 15 cm, the length of AD is ...
A. 3 cm
B. 4 cm
C. 5 cm
D. 6 cm
It was a question for a 9th grader and the book hasn't covered trigonometry by name yet (As in, they don't know about the term sine, cosine, and tangent, but the books do explain the length ratio of triangle which has 45°-90°-45° angle or 30°-60°-90° angle. How to do it and explain it to them?
 

Attachments

  • IMG20191119195818 - Copy.jpg
    IMG20191119195818 - Copy.jpg
    35.9 KB · Views: 116
Mathematics news on Phys.org
Pythagoras $\implies AC = 9$

using the ...

Angle Bisector Theorem

$\dfrac{AD}{AB} = \dfrac{CD}{BC}$

$\dfrac{AD}{12} = \dfrac{9-AD}{15}$

solve for $AD$
 
skeeter said:
Angle Bisector Theorem

$\dfrac{AD}{AB} = \dfrac{CD}{BC}$

Never knew that this theorem exists. Gotta learn how it was derived from now.
 

Similar threads

MHB Could you help me set up these geometric problems?
  • · Replies 2 ·
Replies
2
Views
3K
MHB How can I find the area of a triangle with a given angle and two sides?
  • · Replies 2 ·
Replies
2
Views
1K
MHB Proving Equality of Angles in an Acute Triangle
  • · Replies 4 ·
Replies
4
Views
1K
MHB Act.ge.5 third angle of triangle
  • · Replies 1 ·
Replies
1
Views
1K
MHB [ASK] Find the ratio of the area of triangle BCH and triangle EHD
  • · Replies 4 ·
Replies
4
Views
2K
MHB Length of sides of right triangle with 1 angle and 1 side
  • · Replies 2 ·
Replies
2
Views
2K
MHB Right Isosceles triangle: solve for the length of the unknown legs
  • · Replies 2 ·
Replies
2
Views
1K
MHB How to Find the Length of the Hypotenuse of a Right Triangle?
  • · Replies 8 ·
Replies
8
Views
2K
MHB Can You Find the Angle in This Isosceles Triangle Problem?
  • · Replies 1 ·
Replies
1
Views
1K
MHB Finding the Leg Lengths of a Right Triangle with an Acute Angle of 22°
  • · Replies 2 ·
Replies
2
Views
1K