Question

Find the value of x from the following figure.

Answer 1

Given: Right-angled triangle with base (adjacent to 30°) = 30 m, right angle at left, angle at right = 30°. Let hypotenuse = x.

Step-wise calculation:

1. Use cosine for the 30° angle:

cos 30° = `"Adjacent"/"Hypotenuse"` 

= `30/x` 

`cos 30^circ = sqrt(3)/2`

2. So, `sqrt(3)/2 = 30/x`

3. Solve for x:

`x = 30 xx 2/sqrt(3)` 

= `60/sqrt(3)` 

= `(60sqrt(3))/3` 

= `20sqrt(3)`

4. Decimal: `20sqrt(3)`

= 20 × 1.732

= 34.64 m

x = `20sqrt(3)` m ≈ 34.64 m.