The following diagram shows a triangle ABS, where BC=5,\ \hat{B}=60^{\circ},\

kiki195ms 2021-11-20 Answered
The following diagram shows a triangle ABS, where \(\displaystyle{B}{C}={5},\ \hat{{{B}}}={60}^{{\circ}},\ \hat{{{C}}}={40}^{{\circ}}\). Calculate AB to the nearest whole number.
image

Expert Community at Your Service

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

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question

Expert Answer

Lupe Kirkland
Answered 2021-11-21 Author has 1491 answers
Step 1
The Law of Sines is the relationship between the sides and angles of non-right (oblique) triangles.
Simply, it states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle.
Step 2
Using hte law of sine in \(\displaystyle\triangle{A}{B}{C}\)
\(\displaystyle\Rightarrow{\frac{{{A}{C}}}{{{\sin{{B}}}}}}={\frac{{{A}{B}}}{{{\sin{{C}}}}}}\)
\(\displaystyle\Rightarrow{\frac{{{5}}}{{{\sin{{60}}}^{{\circ}}}}}={\frac{{{x}}}{{{\sin{{40}}}^{{\circ}}}}}\)
\(\displaystyle\Rightarrow{{\sin{{40}}}^{{\circ}}=}{0.643}\) and \(\displaystyle{{\sin{{60}}}^{{\circ}}=}{0.866}\)
\(\displaystyle\Rightarrow{x}={\frac{{{5}\times{\sin{{40}}}^{{\circ}}}}{{{\sin{{60}}}^{{\circ}}}}}={\frac{{{5}\times{0.643}}}{{{0.866}}}}={3.71}{c}{m}\)
\(\displaystyle\Rightarrow{x}={4}{c}{m}\) (to the nearest whole number)
Have a similar question?
Ask An Expert
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 2021-09-06

Given a right triangle, where one cathetus is \(\displaystyle\overline{{A}}={11}\) m, the hypothenuse is \(\displaystyle\overline{{C}}={15}\) m, and \(\displaystyle\angle{c}={90}^{\circ}\) . Find all missing sides \(\displaystyle{\left(\overline{{B}}\right)}\) and angles \(\displaystyle{\left(\angle{a}{\quad\text{and}\quad}\angle{b}\right)}\).

asked 2021-08-31
Given a right triangle with \(\displaystyle\angle{a}={23.4}^{\circ}\). The cathetus opposite to \(\displaystyle\angle{a}\) is \(\displaystyle\overline{{A}}={5.75}\) m. Find the second cathetus \(\displaystyle{\left(\overline{{B}}\right)}\).
asked 2021-11-20
Consider the non-right triangle below.

Suppose that \(\displaystyle{m}\angle{C}{A}{B}={61}^{{\circ}}\), and that \(\displaystyle{x}={35}{c}{m}\) and \(\displaystyle{y}={15}{c}{m}\). What is the area of this triangle?
asked 2021-11-21
Consider the non-right triangle below

Suppose that \(\displaystyle{m}\angle{B}{C}{A}={69}^{{\circ}}\), and that \(\displaystyle{x}={32}{c}{m}\) and \(\displaystyle{y}={49}{c}{m}\). What is the degree measure of \(\displaystyle\angle{A}{B}{C}?\)
asked 2021-11-22
Consider the non-right triangle below

Suppose that \(\displaystyle{m}\angle{A}{C}{B}={98}^{{\circ}}\) and \(\displaystyle{m}\angle{B}{A}{C}={42}^{{\circ}}\), and that \(\displaystyle{y}={51.4}{c}{m}\). What is the value of x?
asked 2021-11-22
Consider the non-right triangle below

Suppose that \(\displaystyle{m}\angle{A}{C}{B}={103}^{{\circ}}\) and \(\displaystyle{m}\angle{B}{A}{C}={44}^{{\circ}}\), and that \(\displaystyle{y}={50.5}{c}{m}\). What is the value of x?
asked 2021-11-22
Consider the non-right triangle below.

Suppose that \(\displaystyle{m}\angle{B}{C}{A}={70}^{{\circ}}\), and that \(\displaystyle{x}={33}{c}{m}\) and \(\displaystyle{y}={47}{c}{m}\) What is the degree measure of \(\displaystyle\angle{A}{B}{C}?\)

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question
...