angle of elevation of two ships from the top of the lighthouse and on the same side are fond to be 45&30 dreege respectively if the ship is 200m apart find the height of the lighthouse
X1 = ?
X2 = 200.
h = X1*Tan45 = (X1+200)*Tan30.
To find the height of the lighthouse, we can use trigonometry, specifically the tangent function.
Let's assign variables:
1. Let 'h' be the height of the lighthouse.
2. Let 'd' be the distance between the two ships, which is given as 200m.
3. Let 'θ₁' be the angle of elevation from the top of the lighthouse to the first ship, which is given as 45 degrees.
4. Let 'θ₂' be the angle of elevation from the top of the lighthouse to the second ship, which is given as 30 degrees.
Now, let's use the tangent function to find the height of the lighthouse.
The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle.
For the first ship:
We have the opposite side as 'h' and the adjacent side as 'd'.
So, tan(θ₁) = h / d.
For the second ship:
We have the opposite side as 'h' and the adjacent side as 'd'.
So, tan(θ₂) = h / d.
Now, let's solve these equations to find the value of 'h'.
Using the given values:
tan(45 degrees) = h / 200
tan(30 degrees) = h / 200
Using a calculator, we can find that:
tan(45 degrees) ≈ 1.00
tan(30 degrees) ≈ 0.58
Substituting the values:
1.00 = h / 200
0.58 = h / 200
Now, let's solve these equations to find the value of 'h'.
For the first equation:
h = 1.00 * 200
h = 200m
For the second equation:
h = 0.58 * 200
h ≈ 116m
Therefore, the height of the lighthouse is approximately 116 meters.