Mathematics: If a distance of 75 yds is measured back from the edge of the canyon and two angles are measured , find the distance across the canyon angle acb = 50° angle abc=100° a=75 yds what does c equal?

If a distance of 75 yds is measured back from the

Ответ:

babyari18

09.03.2022

Mathematics

Length of side :

$c = \rm AB \approx 115\; yds$ .

The distance across the canyon is approximately

$\rm 113\;yds$ .

Step-by-step explanation:

is the length of the side opposite to the angle $\rm A\hat{C} B$ .

is the length of the side opposite to the angle $\rm B\hat{A}C$ .

Apply the law of sine:

$\displaystyle \frac{c}{\sin{\rm A\hat{C}B} = \frac{a}{\sin{\rm B\hat{A}C}}$ .

In other words,

$\displaystyle c = \sin{\rm B\hat{A}C} \cdot \frac{a}{\sin{\rm A\hat{C} B}}$ .

However, the value of the angle $\rm B\hat{A}C$ isn't given. Don't panic. The three interior angles of a triangle shall add up to 180°. Two of the three angles are given. The value of the third angle is implied.

$\rm B\hat{A}C = 180\textdegree{} - A\hat{C}B - A\hat{B}C = 30\textdegree{}$ .

Apply the law of sine to find :

$\displaystyle \begin{aligned}c &= \sin{\rm A\hat{C}B} \cdot \frac{a}{\sin{\rm B\hat{A}C}}\\ &= \sin{50\textdegree{}}\cdot \frac{\rm 75\; yds}{\sin{30\textdegree{}}}\\ &\rm = 114.907\; yds\end{aligned}$ .

Refer to the diagram. The distance across the canyon will be

$\rm AB \cdot \sin{A\hat{B}C} = 114.907\times \sin{100\textdegree{}} \approx 113\;yds$ .

If a distance of 75 yds is measured back from the edge of the canyon and two angles are measured , f

0,0(0 оценок)

If a distance of 75 yds is measured back from the edge of the canyon and two angles are measured , find the distance across the canyon angle acb = 50° angle abc=100° a=75 yds what does c equal?

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question