Answer:
x = 20
Step-by-step explanation:
These angles are equal to each other because they are vertical angles.
Hence, we can equal the two measurements together to solve for x:
3x + 50 = 6x - 10
3x + 60 = 6x
60 = 3x
20 = x
Check your work:
3(20) + 50 = 6(20) - 10
60 + 50 = 120 - 10
110 = 110
Correct
Answer:
32
Step-by-step explanation:
Answer:
Step-by-step explanation:
Let the base camp is point A and boats' locations after two hours are points B and C.
By connecting the three points together we get a triangle ABC with sides:
- AB = 50*2 = 100 km
- AC = 70*2 = 140 km
The angle between AB and AC is:
- 60 + 50 = 110 degrees (opposite directions from south)
We are looking for the distance BC, which can be found by using the law of cosines:
- BC² = AB² + AC² - 2AB*AC*cos ∠BAC
- BC² = 100² + 140² - 2*100*140*cos 110°
- BC² = 39176.56 (rounded)
- BC = √39176.56 = 197.93 km (rounded)
The distance between the boats is 197.93 km.
The product should be 792.65
This should be your answer
