triangle ABC is a right triangle with its right angle

Ashley Searcy 2021-11-27 Answered
triangle ABC is a right triangle with its right angle at C. The bisector of angle B intersects AC at D. The bisector of the exterior angle at B intersects AC at E. If BD= 15 and BE=20, what are the lengths of triangle ABC?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Marian Tucker
Answered 2021-11-28 Author has 7539 answers
Step 1
Using basic properties of triangles we can solve this question.
image
Step2
angle abc is bisected by bd
angle abg is bisected by be
angle dbe=90(half of a angle in a straight line)
bd=15cm
be=20cm
By pythagoras theorem,
de=25cm
Let de=xcm
\(\displaystyle{b}{e}=\sqrt{{{b}{e}^{{{2}}}-{c}{e}^{{{2}}}}}\)
\(\displaystyle=\sqrt{{{b}{d}^{{{2}}}-{d}{c}^{{{2}}}}}\)
\(\displaystyle={12}{c}{m}\)
Step 3
\(\displaystyle\angle{d}{b}{c}={\frac{{{d}{c}}}{{{b}{c}}}}\)
\(\displaystyle={\frac{{{9}}}{{{12}}}}\)
\(\displaystyle{d}{c}={x}\)
\(\displaystyle{e}{c}={25}-{x}\)
\(\displaystyle{b}{e}^{{{2}}}-{c}{e}^{{{2}}}={b}{d}^{{{2}}}-{x}^{{{2}}}\)
\(\displaystyle{x}={d}{c}\)
\(\displaystyle={9}{c}{m}\)
\(\displaystyle\angle{a}{b}{c}={2}\angle{0}{b}{c}\)
\(\displaystyle={\frac{{{24}}}{{{7}}}}\)
\(\displaystyle{\frac{{{24}}}{{{7}}}}={\frac{{{y}}}{{{12}}}}\)
\(\displaystyle{y}={\frac{{{24}\star{12}}}{{{7}}}}\)
\(\displaystyle{a}{c}={\frac{{{288}}}{{{7}}}}\)
By pythagoras theorem
\(\displaystyle{a}{c}^{{{2}}}+{b}{c}^{{{2}}}={a}{b}^{{{2}}}\)
\(\displaystyle{a}{b}={\frac{{{300}}}{{{7}}}}\)
Not exactly what you’re looking for?
Ask My Question
0
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-11-17
Triangles ABC and DEF are right triangles, as shown \(\displaystyle\triangle{A}{B}{C}\) is similar to \(\displaystyle\triangle{D}{E}{F}\)

Which ratios are equal to \(\displaystyle{\cos{{\left({B}\right)}}}\)? Choose the TWO ratios that apply.
asked 2021-11-29
Triangles ABC and DEF are right triangles, as shown. \(\displaystyle\triangle{A}{B}{C}\) is similar to \(\displaystyle\triangle{D}{E}{F}\).
Which ratios are equal to \(\displaystyle{\cos{{\left({B}\right)}}}\) ? Choose the TWO ratios that apply.
asked 2021-11-25
The perpendicular bisector \(\displaystyle\overline{{{A}{B}}}\) in the right triangle \(\displaystyle\triangle{A}{B}{C}\) forms the triangle with the area 3 times smaller than the area of \(\displaystyle\triangle{A}{B}{C}\). Find the measures of acute angles in \(\displaystyle\triangle{A}{B}{C}\)
asked 2021-09-04
Given a right triangle with \(\displaystyle\angle{a}={65}^{\circ}\). The cathetus opposite to \(\displaystyle\angle\)a is \(\displaystyle\overline{{A}}={250}\) m. Find the second cathetus \(\displaystyle{\left(\overline{{B}}\right)}\).
asked 2021-09-10
A right triangle with a side cathetuses equal to 12cm and 5 cm. Find the angle opposite to the cm side.
asked 2021-09-10
Given a right triangle. One cathetus is 100cm long. Find the length of the other cathetus, if the angle opposite to it is \(\displaystyle{71.6}^{\circ}\). Round your answer to an integer.
asked 2021-09-12
Given a right triangle. anglea is \(\displaystyle{51}^{\circ}\). A line is drawn from anglec \(\displaystyle{\left({90}^{\circ}\right)}\) to the hypotenuse, creating a \(\displaystyle{7}^{\circ}\) angle between the line and the cathetus adjusted to angleb. The cathetus adjusted to angel is 47cm. Find the length of the line drawn.
...