Question

50 POINTS GIVING BRAINLIEST

Draft a small paragraph Explaining the concept of ground speed and horizontal distance traveled or distance traveled over the earth. Consider in your description what information is needed to calculate distance traveled.

Answer 1

Answer:

miles to travel directly south = 54 miles (to the nearest mile)

extra miles = 68 miles (nearest mile)

Step-by-step explanation:

We need to find the height of the right triangle in the diagram.

To do this, use the sine trig ratio.

$\sin(x)=\sf\dfrac{O}{H}$

where:

• $x$ is the angle
• O is the side opposite the angle
• H is the hypotenuse

Given:

$x$ = 27°

O = height (h)

H = 120 miles

Substituting the given values into the formula:

$\implies \sin(27^{\circ})=\sf\dfrac{h}{120}$

$\implies \sf h=120 \sin(27^{\circ})$

$\implies \sf h=54.47885997...$

Therefore, the shipmate will have to travel 54 miles (to the nearest mile) directly south.

To find the number of extra miles have been traveled, we first need to find the base length of the right triangle.

To do this, use the cos trig ratio.

$\cos(x)=\sf\dfrac{A}{H}$

where:

• $x$ is the angle
• A is the side adjacent the angle
• H is the hypotenuse

Given:

• $x$ = 27°
• A = base (b)
• H = 120 miles

Substituting the given values into the formula:

$\implies \cos(27^{\circ})=\sf\dfrac{b}{120}$

$\implies \sf b=120 \cos(27^{\circ})$

$\sf \implies b=106.9207829...$

Therefore, the base of the right triangle is 106.9207829... miles

To find the extra miles, sum the hypotenuse and the height of the triangle, then subtract the base.

Extra miles = (120 + 54.47885997... ) - 106.9207829...

                  = 67.55807707...

                  = 68 miles (nearest mile)

Answer 2

#1

Apply sines

• sin27=Perpendicular/Hypotenuse
• 0.45399=P/120
• P=120(0.45399)
• P=54.5ft

#2

Total distance travelled =120+54.5=174.5ft

Base:-

• cos27=B/120
• 0.89=B/120
• B=120(0.89)
• B≈106ft

Extra distance:-

• 174.5-106
• 68.5ft