Two boats 70 metres apart are on opposite side of a lighthouse from the two boats are 71.6° and 45°.Find the height of the lighthouse (tan 71.6°=3)
Come help!! me at mate my teacher is depriving me of my 4 marks because of this same quesion
tan 71.6 = h/x = 3
tan 45 = h / (70-x) = 1
so
x = h/3
and
70 - x = h
so
70 - h/3 = h = 3 h/3
70 = 4 h/3
h = 210 / 4 = 52.5
To find the height of the lighthouse, we can use trigonometry. Let's assume the height of the lighthouse is represented by 'h'.
We have two boats, 70 meters apart, on opposite sides of the lighthouse. The angles of elevation from the boats to the top of the lighthouse are 71.6° and 45°, respectively.
Using trigonometry, we can use the tangent function since we know the angle and height of the lighthouse.
tan(angle) = opposite/adjacent
So, for the first boat with an angle of 71.6°:
tan(71.6°) = h/70
Given that tan(71.6°) = 3, we can substitute this value into the equation:
3 = h/70
Multiplying both sides of the equation by 70, we get:
h = 3 * 70
h = 210
Therefore, the height of the lighthouse is 210 meters.
To find the height of the lighthouse, we can use trigonometry and the given angles. Let's break down the problem step by step:
Step 1: Draw a diagram
Draw a diagram representing the scenario. Label the positions of the two boats and the lighthouse, and label the distance between the boats as 70 meters.
B1 L B2
|-----------------|--------------|
71.6° 45°
Step 2: Determine the distance from the lighthouse to each boat
Since the two boats are on opposite sides of the lighthouse, the distance from the lighthouse to each boat is the same. Let's call this distance "d".
Step 3: Apply trigonometry
From the diagram, we can see that we have a right-angled triangle between each boat and the lighthouse. We can use the tangent function to find the height of the lighthouse (which is equal to the distance "d").
In the triangle involving B1, L, and the distance "d":
tan(71.6°) = height of the lighthouse (d) / 70
In the triangle involving B2, L, and the distance "d":
tan(45°) = height of the lighthouse (d) / 70
Step 4: Solve for the height of the lighthouse (d)
From the given information, we know that tan(71.6°) = 3. Substituting this into the equation from Step 3 involving B1:
3 = d / 70
To solve for d, we can multiply both sides of the equation by 70:
3 * 70 = d
So, d = 210 meters.
Therefore, the height of the lighthouse, which is equal to the distance "d", is 210 meters.