Homework Help

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

user profile pic

novjb | (Level 1) Salutatorian

Posted August 2, 2013 at 1:11 AM via web

dislike 1 like

Solve for x, y, and z.

Thank you for your help.

1 Answer | Add Yours

user profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted August 2, 2013 at 1:35 AM (Answer #1)

dislike 1 like

(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).

`x=tan^(-1)(28/45)~~31.8907918`

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^@`

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes