Question

PLEASE HELP Solve the right triangle.


Round your answers to the nearest tenth.

Answer 1

• a = 10.724
• b = 8.988
• A = 40°

Explanation:

Here we are given with a right angled traingle and we are interested in finding

• Angle A
• side “ a ”
• side “ b ”

Firstly we can use the ratio of sine to find the side a , as ;

`\longrightarrow \sin\theta =(p)/(h)`

Substituting the respective values,

`\longrightarrow \sin50^\circ =(a)/(14)`

Put on the value of sin50° = 0.766 ;

`\longrightarrow 0.766 =(a)/(14)`

Cross multiply ,

`\longrightarrow a = 14* 0.766`

Simplify,

`\longrightarrow \underline{\underline{\boldsymbol{ a = 10.724 \approx 10.8}}}`

____________________________

Now for finding b , we may use the ratio of cosine as ,

`\longrightarrow \cos\theta =(b)/(h)`

Substituting the respective values,

`\longrightarrow \cos50^\circ =(b)/(14)`

Put on the value of cos50° = 0.642 ;

`\longrightarrow 0.642 =(b)/(14)`

Cross multiply,

`\longrightarrow b =14* 0.642`

Simplify,

`\longrightarrow \underline{\underline{\boldsymbol{ b = 8.988 \approx 9}}}`

______________________________

Again we know that the sum of three angles of a triangle is 180° . So that;

`\longrightarrow A +50^\circ +90^\circ =180^\circ`

Solve for A ,

`\longrightarrow A =180^\circ -140^\circ`

`\longrightarrow \underline{\underline{\boldsymbol{ A = 40^\circ }}}`

And we are done!