PLEASE HELP Solve the right triangle. Round your answers to the nearest tenth.

Question

asked Nov 7, 2023 199k views

1 Answer

Bill Menees · Answer 1 · 2023-11-13T16:21:37+0000

Answer:

Explanation:

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

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,

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

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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,

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

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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!