Question

Find the value of x to the nearest tenth.

Answer 1

The value of x is 11.

Explanation:

From the figure it is clear that the given triangle is a right angled triangle. The length of hypotenuse is x units , an angle 35° and adjacent side is 9 units.

Using trigonometric ratios, in a right angled triangle,

`\cos \theta = (adjacent)/(hypotenuse)`

Substitute θ=35, adjacent = 9, hypotenuse =x in the above equation.

`\cos 35=(9)/(x)`

`0.819=(9)/(x)`

Multiply both sides by x.

`0.819x=9`

Divide both sides by 0.819.

`x=(9)/(0.819)`

`x=10.989\approx 11`

Therefore the value of x is 11.

Answer 2

cos(angle) = Adjacent Leg / Hypotenuse

cos(35) = 9 / x

x = 9 / cos(35)

x = 10.99

Rounded to nearest tenth = 11.0