If an ant is 100 feet away from a tree growing straight up, and the ant has to look up at an angle of 68 degrees to see the top of the tree, how tall is the tree? Select the closest answer.Question 34Select one:a.200 feetb.140 feetc.80 feetd.20 feete.10 feet
Question
If an ant is 100 feet away from a tree growing straight up, and the ant has to look up at an angle of 68 degrees to see the top of the tree, how tall is the tree? Select the closest answer.Question 34Select one:a.200 feetb.140 feetc.80 feetd.20 feete.10 feet
Solution
To solve this problem, we can use the tangent function in trigonometry. The tangent of an angle in a right triangle is equal to the opposite side (the height of the tree in this case) divided by the adjacent side (the distance from the ant to the tree in this case).
So, we have:
tan(68 degrees) = height / 100 feet
To find the height, we rearrange the equation to:
height = tan(68 degrees) * 100 feet
Using a calculator, tan(68 degrees) is approximately 2.40. So,
height = 2.40 * 100 feet = 240 feet
However, 240 feet is not one of the options. The closest option to 240 feet is 200 feet. So, the answer is:
a. 200 feet
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