you are standing 40m from the base of a tree leaning 8 degree from the vertical away from you. the angle o elevation from your feet to the top of the tree is 20 seconds and 50 minutes find the height of the tree.
To find the height of the tree, we can use trigonometric functions. Let's break down the problem step-by-step:
1. Convert the angle of elevation from seconds and minutes to decimal form:
20 seconds = 20/3600 = 0.0056 degrees
50 minutes = 50/60 = 0.8333 degrees
2. Calculate the angle of elevation in degrees:
Angle of elevation = 0.0056 degrees + 0.8333 degrees = 0.8389 degrees
3. Draw a diagram to visualize the problem. The tree is leaning away from you, so the angle from the vertical to the tree is 8 degrees. The angle of elevation from your feet to the top of the tree is 0.8389 degrees.
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40m\ tree
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4. Use trigonometric functions to find the height of the tree:
tan(angle of elevation) = height of tree / distance from the base of the tree
tan(0.8389 degrees) = height of tree / 40m
Rearrange the equation to solve for the height of the tree:
height of tree = tan(0.8389 degrees) * 40m
5. Calculate the height of the tree:
height of tree = tan(0.8389 degrees) * 40m
Using a scientific calculator, we find that tan(0.8389 degrees) ≈ 0.01466.
height of tree ≈ 0.01466 * 40m
height of tree ≈ 0.5864m
Therefore, the height of the tree is approximately 0.5864 meters.
To find the height of the tree, we can use trigonometry.
Step 1: Convert the angle of elevation from seconds and minutes to degrees. There are 60 seconds in a minute and 60 minutes in a degree, so 20 seconds and 50 minutes can be written as (20/60) + (50/60)/60 = 0.347 degrees.
Step 2: Draw a diagram to visualize the problem. Place the tree as a vertical line and draw a right triangle with the tree as the height (h), the distance from your feet to the tree as the base (40m), and the angle of elevation (8 degrees).
Step 3: Identify the relevant trigonometric ratios. In this case, the tangent ratio (opposite/adjacent) is the most useful. We have the opposite side (height of the tree) and the adjacent side (distance from your feet to the tree).
Step 4: Apply the tangent ratio to find the height of the tree. The formula is tan(angle) = opposite/adjacent. Substituting the known values, we get tan(8 degrees) = h/40.
Step 5: Solve for h. Rearranging the equation, h = 40 * tan(8 degrees).
Using a calculator, we can find the height of the tree: h ≈ 6.04 meters.
Therefore, the height of the tree is approximately 6.04 meters.
assuming you meant 20°50' and not 20"50', draw the diagram, filling in the angles. Use the law of sines to find h:
40/sin61°10' = h/sin20°50'