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
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: 109
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 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'Useless continued fraction for 1'

I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
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

Hot Threads

Recent Insights

Back
Top