ok so there.s a right triangle

90 degrees on the bottom left, unknown on the bottom right

and the top angle is 58 degrees

the bottom side is 4.0 in length and the other sides are unknown

solve for all sides and angles

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- Aug 2nd 2010, 01:05 PMgabrielright triangle trig cont. w/ questions
ok so there.s a right triangle

90 degrees on the bottom left, unknown on the bottom right

and the top angle is 58 degrees

the bottom side is 4.0 in length and the other sides are unknown

solve for all sides and angles - Aug 2nd 2010, 01:31 PMlvleph
You can use the facts $\displaystyle \sin \theta = \dfrac{Opposite}{Hypotenuse}\; \cos \theta = \dfrac{Adjacent}{Hypotenuse}\; \tan \theta = \dfrac{Opposite}{Adjacent}$

To get you started $\displaystyle \sin 58^{\circ} = \dfrac{4}{c}$ assuming $\displaystyle c$ is the hypotenuse. Now solve for $\displaystyle c$. You could now solve for the remaining side with either the pythagorean theorem or the cosine relation.

For the angle, use the fact that all angles add to $\displaystyle 180^{\circ}$

EDIT: Fixed some typos. - Aug 2nd 2010, 01:33 PMMath Major
Well, you know that a triangle has 180 degrees, and we've accounted for 90 + 58 = 148 of them. Thus, the remaining angle is 42 degrees.

I'll call your "bottom" side x, your "vertical" side y, and your hypotenuse h (if I'm reading your description right!.

So, $\displaystyle sin(58) = \frac{x}{h} $

But we know x = 4, so

$\displaystyle sin(58) = \frac{4}{h} $.

Can you find y?

Edit: All angles are in degrees. - Aug 2nd 2010, 02:44 PMgabriel
so sin(58) =4/h and then this means that h=4.72 approximately

according to the following: h=4.0(1/sin(58)=4.72=b correct?

but i tried tangent for locating the adjacent side and my answer was 6.40 which is incorrect

what happened? - Aug 2nd 2010, 02:50 PMMath Major
$\displaystyle tan(58) = \frac{4}{y} \implies y = \frac{4}{tan(58)} =~ 2.5$