Question

11. Use a trigonometric ratio to find the length of x in the triangle. Give your answer to two decimal places.

Answer 1

Given :-

• A right angled triangle with two of the sides as x and 9m .
• One of the acute angle is 28°

To Find :-

• The value of x .

Solution :-

As we know that in any right angled triangle ,

`\longrightarrow tan\theta = (perpendicular)/(base)`

In the given triangle , perpendicular is x and the base is 9m . Substituting the respective values ,

`\longrightarrow tan\theta = (x)/(9m)`

Also here ,

`\longrightarrow \theta = 28^o`

So that ,

`\longrightarrow tan28^o = (x)/(9m)`

Substituting the value of tan28° ,

`\longrightarrow 0.53 = (x)/(9m)`

Cross multiply ,

`\longrightarrow x = 9m * 0.53`

Multiply the constants ,

`\longrightarrow\underline{\underline{ x = 4.77m }}`

Hence the value of x is 4.77 m .