Solve for x, y, and z. Thank you for your help.

1 Answer

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embizze | High School Teacher | (Level 2) Educator Emeritus

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(x) We have a right triangle with x one of the acute angles. The leg opposite x is 28 and the leg adjacent to x is 45.

We know the trigonometric relationship `tanalpha="opp"/"adj"` for the acute angles of a right triangle.

`tanx=28/45` To "undo" taking the tangent we take the inverse tangent (or arctangent).


So `x~~31.9^@`

(y) and (z) are acute angles of a right triangle. The leg opposite z (and adjacent to y) is 77 while the hypotenuse is 85.

`sinz="opp"/"hyp"=77/85` so `z=sin^(-1)(77/85)~~64.94238458`

`cosy="adj"/"hyp"=77/85` so `y=cos^(-1)(77/85)~~25.05761542`

Then `y~~25.1^@,z~~64.9^@`