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.

Question

tan θ = 0.7536
Hypotenuse = 29 miles
Opposite side = ?

Answer 1

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).