To solve this problem, we need to use some trigonometry. We can use the tangent function to find the length of the magma below sea level.
Let's define the following variables:
• x: the length of magma below sea level (what we want to find)
• y: the total length of magma (which we don't know)
• θ: the angle of elevation, which is 40°
We can set up a right triangle with the hypotenuse representing the total length of magma (y), the opposite side representing the length of magma below sea level (x), and the adjacent side representing the distance from the volcano to the point where the magma rises above sea level (which we don't need to calculate).
Using the tangent function, we can write:
tan(θ) = x / y
Rearranging this equation, we get:
x = y * tan(θ)
Now we just need to plug in the values we know:
• θ = 40°
• y = 15 kilometers (since the magma reservoir is located 15 kilometers beneath the Chijiwa Bay)
Using a calculator, we can evaluate tan(40°) to be approximately 0.8391.
Plugging in these values, we get:
X = 15km*0.8391, X = 12.5865km
Therefore, the length of magma below sea level is approximately 12.5865 kilometers