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.
Hypotenuse = 14.5 meters
Opposite side = 6.3 meters
θ = ?
To solve for the missing angle, you can use the sine function:
sin(θ) = Opposite / Hypotenuse
Substituting the known values:
sin(θ) = 6.3 / 14.5
θ = arcsin(6.3 / 14.5)
Using a calculator, the value of θ is approximately 25.6174 degrees.
To find the missing angle θ in a right triangle, we can use the trigonometric function of sine (sin).
The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.
sin(θ) = Opposite/Hypotenuse
Given the values:
Hypotenuse = 14.5 meters
Opposite side = 6.3 meters
We can plug in these values into the formula:
sin(θ) = 6.3/14.5
Now, we can solve for θ by taking the inverse sine of both sides of the equation.
θ = sin^(-1)(6.3/14.5)
Using a calculator, the inverse sine of 6.3/14.5 is approximately 24.4343 degrees.
Therefore, θ ≈ 24 degrees (rounded to the nearest degree).