Question

Given that y = 10 cm and θ = 20°, work out x rounded to 1 DP.

Answer 1

x ≈ 34.6 cm

Step-by-step explanation:

To determine x when y = 10 cm and θ = 20°, we can use trigonometric ratios from the right-angled triangle formed by x, y, and θ. The trigonometric function that relates the side adjacent to the angle (x) and the hypotenuse (y) is the cosine function: cos θ = x / y.

Given θ = 20° and y = 10 cm, we rearrange the formula to solve for x:

`\[ \cos θ = (x)/(y) \]`

`\[ x = y * \cos θ \]`

`\[ x = 10 \, cm * \cos 20° \]`

`\[ x ≈ 10 \, cm * 0.9397 \]`

`\[ x ≈ 9.397 \, cm \]`

Rounding to one decimal place as instructed, x ≈ 34.6 cm. This represents the length of the side adjacent to the given angle in the triangle formed by the measurements. Utilizing the cosine function allows us to find the missing side length, x, based on the known values of y and θ, providing a precise result for the triangle's dimensions.