Question
Using the info given, solve for the missing value of the right triangle. Round each angle to the nearest degree, each length to the nearest tenth, & each trigonometric value to four decimal places, if necessary.
tan θ = 0.7536
Hypotenuse = 29 miles
Opposite side = ?
tan θ = 0.7536
Hypotenuse = 29 miles
Opposite side = ?
Answers
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To find the length of the opposite side, we can use the formula for tangent:
tan(θ) = opposite/adjacent
In this case, the angle θ is not given, but the value of tangent is provided as 0.7536. We can use the inverse tangent function (arctan) to find the angle:
θ = arctan(0.7536)
Using a calculator, we find that θ is approximately 36.8699 degrees.
Now, we can use the given angle and the length of the hypotenuse to find the length of the opposite side using the sine function:
sin(θ) = opposite/hypotenuse
Opposite side = sin(θ) * hypotenuse
Opposite side = sin(36.8699) * 29
Using a calculator, we find that the length of the opposite side is approximately 17.6 miles (rounded to the nearest tenth).
tan(θ) = opposite/adjacent
In this case, the angle θ is not given, but the value of tangent is provided as 0.7536. We can use the inverse tangent function (arctan) to find the angle:
θ = arctan(0.7536)
Using a calculator, we find that θ is approximately 36.8699 degrees.
Now, we can use the given angle and the length of the hypotenuse to find the length of the opposite side using the sine function:
sin(θ) = opposite/hypotenuse
Opposite side = sin(θ) * hypotenuse
Opposite side = sin(36.8699) * 29
Using a calculator, we find that the length of the opposite side is approximately 17.6 miles (rounded to the nearest tenth).