From the top of a tower,the angle of depression of a boat is 30degree if the tower is 20cm high how far is the boat from the foot of the tower
From your diagram, you should see than
tan30° = 20/x, where x is the distance you need.
However, a tower 20 cm high ????
You probably meant 20 metres.
30
To find the distance from the foot of the tower to the boat, we can use trigonometry.
Let's label the given information:
- The angle of depression is 30 degrees.
- The height of the tower is 20 cm.
In this scenario, the angle of depression is the angle between the horizontal line (the ground) and the line of sight from the top of the tower to the boat.
To find the distance from the foot of the tower to the boat, we need to consider the right triangle formed by the tower, the boat, and the ground.
In a right triangle, we can use the tangent function, which is defined as the length of the opposite side divided by the length of the adjacent side.
In this case:
- The opposite side is the height of the tower (20 cm).
- The adjacent side is the distance from the foot of the tower to the boat (let's call it x).
So, tan(30°) = 20 cm / x
We can solve this equation for x by rearranging it:
x = 20 cm / tan(30°)
Now, let's calculate the value of x:
Step 1: Convert the angle from degrees to radians (angle in radians = angle in degrees * π/180)
θ = 30° * π/180 = π/6 rad
Step 2: Calculate the tangent value for the angle (tan(θ) = opposite / adjacent)
tan(π/6) = 20 cm / x
Step 3: Rearrange the equation to solve for x
x = 20 cm / tan(π/6)
Step 4: Substitute the value of tan(π/6) using a calculator:
x ≈ 20 cm / 0.5774
Step 5: Calculate the value of x:
x ≈ 34.64 cm
Therefore, the distance from the foot of the tower to the boat is approximately 34.64 cm.