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.
Adjacent side = 26 cm
Hypotenuse = 53 cm
Opposite side = ?
To solve for the missing value of the right triangle, we can use the trigonometric functions sine, cosine, and tangent.
Given:
Adjacent side = 26 cm
Hypotenuse = 53 cm
Let's find the opposite side using the sine function.
sin(angle) = opposite / hypotenuse
sin(angle) = opposite / 53
Rearranging the equation, we get:
opposite = sin(angle) * 53
Now, we need to find the angle. We can use the inverse sine function.
sin^(-1)(opposite / hypotenuse) = angle
Let's calculate the angle:
angle = sin^(-1)(26 / 53) ≈ 30.21 degrees (rounded to the nearest degree)
Now, let's solve for the opposite side:
opposite = sin(angle) * 53
opposite = sin(30.21) * 53
opposite ≈ 26.79 cm (rounded to the nearest tenth)
Therefore, the missing value, the length of the opposite side, is approximately 26.8 cm.
To solve for the missing value of the right triangle, we can use the trigonometric functions sine, cosine, and tangent.
Given:
Adjacent side = 26 cm
Hypotenuse = 53 cm
Opposite side = ? (let's denote it as x)
Based on the given information, we can use the cosine function to find the missing side.
cos(theta) = Adjacent / Hypotenuse
Plugging in the values, we have:
cos(theta) = 26 / 53
Now, let's solve for the angle (theta) using the inverse cosine function.
theta = cos^(-1)(26 / 53)
Calculating this on a calculator, we find that the angle (theta) is approximately 58.7631 degrees.
Next, we can use the sine function to find the value of the missing side.
sin(theta) = Opposite / Hypotenuse
Plugging in the known values, we have:
sin(58.7631 degrees) = x / 53
Now, let's solve for x.
x = sin(58.7631 degrees) * 53
Calculating this on a calculator, we find that the missing side, x, is approximately 44 cm.
Therefore, the approximate value of the missing side (opposite side) is 44 cm.