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.
Adjacent side = 26 cm
Hypotenuse = 53 cm
Opposite side = ?

Answer 1

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.