a submarine at the surface of the ocean makes an emergency dive, its path making an angle of 21 degree with the surface. if it goes 300m long its download path, how deep will it be? what horizontal distance is it from its starting point?
simple sine and cosine ratio problem
sin 21 = depth/300
depth = 300sin21°
= 10.75 m
cos 21 = horizontal distance/ 300
hd = 300cos21 = 280.07 m
To find the depth reached by the submarine and the horizontal distance from its starting point, we can use trigonometry.
1. Depth of the submarine:
The depth of the submarine can be found using the sine of the angle made with the surface.
sin(θ) = opposite/hypotenuse, where θ is the angle made with the surface.
sin(21°) = depth/300m
depth = sin(21°) * 300m
depth ≈ 104.4m
Therefore, the submarine will be approximately 104.4 meters deep.
2. Horizontal distance from the starting point:
The horizontal distance covered by the submarine can be found using the cosine of the angle made with the surface.
cos(θ) = adjacent/hypotenuse, where θ is the angle made with the surface.
cos(21°) = horizontal distance/300m
horizontal distance = cos(21°) * 300m
horizontal distance ≈ 275.6m
Therefore, the submarine will be approximately 275.6 meters from its starting point in the horizontal direction.
To determine the depth and horizontal distance of the submarine, we can use trigonometry. Let's break down the problem step by step:
1. Depth of the submarine:
The vertical distance (depth) can be found using the trigonometric function sine (sin). We know the angle and the length of the downward path, so we can use the equation:
Depth = Length * sin(Angle)
Plugging in the values:
Depth = 300m * sin(21°)
Depth ≈ 107.8m
Therefore, the submarine will be approximately 107.8 meters deep.
2. Horizontal distance from the starting point:
The horizontal distance can be found using the trigonometric function cosine (cos). We know the angle and the length of the downward path, so we can use the equation:
Horizontal Distance = Length * cos(Angle)
Plugging in the values:
Horizontal Distance = 300m * cos(21°)
Horizontal Distance ≈ 277.8m
Therefore, the submarine will be approximately 277.8 meters horizontally away from its starting point.
Hence, the submarine will be approximately 107.8 meters deep and 277.8 meters away from its starting point.