Barb planted a tree and attached a guy wire to help support its growth. If the guy wire is 3.9 m long and is attached at an angle of elevation of 33.5o, how high up the tree will it reach?(Round your answer to 1 decimal place, and put only the number in the box with no units.)
Question
Barb planted a tree and attached a guy wire to help support its growth. If the guy wire is 3.9 m long and is attached at an angle of elevation of 33.5o, how high up the tree will it reach?(Round your answer to 1 decimal place, and put only the number in the box with no units.)
Solution
To solve this problem, we can use the sine function in trigonometry. The sine of an angle in a right triangle is defined as the length of the opposite side divided by the length of the hypotenuse.
In this case, the guy wire is the hypotenuse, the height up the tree is the opposite side, and the angle of elevation is the angle we are interested in.
The formula is: sin(angle) = opposite/hypotenuse
We can rearrange this formula to solve for the opposite side (the height up the tree): opposite = sin(angle) * hypotenuse
Substituting the given values into the formula gives us: opposite = sin(33.5) * 3.9
Now, just calculate the value. Make sure your calculator is set to degrees, not radians, because the angle is given in degrees.
After calculating, round your answer to 1 decimal place.
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