Answer:
The distance across the river from Omkar to the big rock is 131343149 meters
Step-by-step explanation:
* Lets study the information in the problem
- Let Omkar position is point A
- Let Melissa position is point B
- Let big rock position is C on the other side of the river
* Now we have triangle ABC
- The distance between Omkar and Melissa is 100100100 meters
along the river
- The angle between Omkar and the big rock is angle BAC
∴ m∠BAC = 33°
- The angle between Melissa and the big rock is angle ABC
∴ m∠ABC = 98°
- The big rock is at angle C
* Now we can find the distance between Omkar and the big rock
by finding the length of side AC in the triangle
- By using the sine rule
∵ sin A/BC = sin B/AC = sin C/AB
∵ AB = 100100100 meters
∵ m∠ABC = 98°
- Lets find m∠C
∵ In any triangle the sum of the measures of the interior angles is 180°
∴ m∠A + m∠B + m∠C = 180°
∵ m∠A = 33° , m∠B = 98°
∴ 33° + 98° + m∠C = 180° ⇒ add
∴ 131° + m∠C = 180° ⇒ subtract 131 from both sides
∴ m∠C = 49°
- Now lets use the sine rule
∵ sin ABC/AC = sin C/AB
∴ sin 98/AC = sin 49/100100100 ⇒ by using cross multiplication
∴ AC = (sin 98 × 100100100) ÷ sin 49 = 131343148.8
∴ AC ≅ 131343149 meters
* The distance across the river from Omkar to the big rock is
131343149 meters
Answer:
The distance across the river from Omkar to the big rock is 72 meters.
Step-by-step explanation:
Using the given information draw as triangle as shown below.
According to angle sum property, the sum of interior angles of a triangle is 180°.
In triangle ABC,
[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]
[tex]98^{\circ}+33^{\circ}+\angle C=180^{\circ}[/tex]
[tex]131^{\circ}+\angle C=180^{\circ}[/tex]
[tex]\angle C=180^{\circ}-131^{\circ}=49^{\circ}[/tex]
The measure of angle C is 49°.
Sine formula:
[tex]\frac{a}{\sin a}=\frac{b}{\sin b}=\frac{c}{\sin c}[/tex]
Using sine formula in triangle ABC, we get
[tex]\frac{AC}{\sin B}=\frac{AB}{\sin C}[/tex]
[tex]\frac{AC}{\sin 33^{\circ}}=\frac{100}{\sin 49^{\circ}}[/tex]
[tex]AC=\frac{100}{\sin 49^{\circ}}\times \sin 33^{\circ}[/tex]
[tex]AC=\frac{100}{0.7547}\cdot0.544639[/tex]
[tex]AC=72.166[/tex]
[tex]AC\approx 72[/tex]
Therefore the distance across the river from Omkar to the big rock is 72 meters.
