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 = 255 ft
θ = 25°
Adjacent side = ?
To find the adjacent side of the right triangle, we can use the cosine ratio. The cosine ratio states that the cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse.
cos(θ) = adjacent/hypotenuse
In this case, θ is given as 25° and the hypotenuse is 255 ft. Let's calculate the adjacent side:
cos(25°) = adjacent/255
To solve for the adjacent side, we can rearrange the equation:
adjacent = cos(25°) * 255
Using a calculator, the cosine of 25° is approximately 0.9063. Multiplying this by 255, we find:
adjacent ≈ 0.9063 * 255 ≈ 231.0925
Rounding to the nearest tenth, the length of the adjacent side is approximately 231.1 ft.
To find the missing value of the right triangle, we can use the trigonometric ratio: cosine (θ) = adjacent/hypotenuse
Given:
Hypotenuse = 255 ft
θ = 25°
So, we can solve for the adjacent side.
Step 1: Substitute the given values into the equation:
cos(θ) = adjacent/hypotenuse
cos(25°) = adjacent/255 ft
Step 2: Calculate the cosine of 25°:
cos(25°) ≈ 0.9063
Step 3: Solve for the adjacent side:
0.9063 = adjacent/255 ft
To find the adjacent side, we can cross-multiply:
0.9063 * 255 ft = adjacent
Adjacent ≈ 231.3315 ft
Therefore, the adjacent side of the right triangle is approximately 231.3 ft.