Because of the prevailing winds, a tree grew so that it was leaning 6° from the vertical. At a point 100 feet away from the tree, the angle of elevation to the top of the tree is 22°55'
Thanks. Do you have a question on this?
To find the height of the tree, we can use basic trigonometry. Let's break down the problem step by step:
Step 1: Draw a diagram
Draw a diagram representing the situation described in the problem. Label the relevant angles and distances.
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| T (top of the tree)
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/ | 100 ft
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A B (base of the tree)
Step 2: Identify the right triangle
We can see that triangle ATB is a right triangle. We can utilize the angle of inclination of the tree and the angle of elevation to the top of the tree to find the height.
Step 3: Use trigonometry
In triangle ATB, we can use the tangent function to find the height (h) of the tree.
tan(angle of inclination of the tree) = h / 100 ft
Now, let's convert the angle of inclination from degrees to radians for our calculations.
angle of inclination (in radians) = 6° * (π/180)
Step 4: Calculate the height
Using the tangent function, we can now calculate the height (h) of the tree.
h = tan(angle of inclination (in radians)) * 100 ft
Step 5: Round the answer
Round the height to an appropriate number of decimal places based on the level of precision required in the problem.
Step 6: Substitute the values and solve
Now, substitute the values into the formula and calculate the height of the tree:
angle of inclination (in radians) = 6° * (π/180) = 0.10472 radians
h = tan(0.10472) * 100 ft
Using a calculator or math software, calculate the value of tan(0.10472), and then multiply the result by 100 ft to get the height of the tree.
The final answer will give you the height of the tree.