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SCORPION-xisa [38]
3 years ago
7

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?

Mathematics
1 answer:
adelina 88 [10]3 years ago
3 0

Answer:

Length of side c:

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

The distance across the canyon is approximately

\rm 113\;yds.

Step-by-step explanation:

  • c is the length of the side opposite to the angle \rm A\hat{C} B.
  • a 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 c:

\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.

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muminat

Answer: 14/25 = 56/100

               11/20 =  55/100

               14/25 > 11/20

Step-by-step explanation:

The least common multiple of 20 and 25 is 100.

(100 = 20*5, 25*4)

So we can take the common denominator 100.

14*4/25*4 =56/100. ∴14/25 = 56/100

11*5/20*5  =55/100. ∴11/20  = 55/100

56>55

∴56/100 > 55/100

∴14/25 > 11/20

Hope it's good;)

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