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

  • Thread starter Thread starter Monoxdifly
  • Start date Start date
  • Tags Tags
    Angle Triangle
Click For Summary
In a right triangle ABC with a right angle at A and angle bisector BD, the lengths AB and BC are given as 12 cm and 15 cm, respectively. To find the length of segment AD, the Angle Bisector Theorem is applied, leading to the equation AD/12 = (9 - AD)/15. Solving this equation reveals that AD equals 6 cm. The discussion highlights the importance of understanding the Angle Bisector Theorem, especially for students who have not yet learned trigonometry. This approach provides a foundational method for solving problems involving right triangles and angle bisectors.
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: 112
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.
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »

Similar threads

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