# right triangle trig cont. w/ questions

• Aug 2nd 2010, 01:05 PM
gabriel
right 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 PM
lvleph
You can use the facts $\sin \theta = \dfrac{Opposite}{Hypotenuse}\; \cos \theta = \dfrac{Adjacent}{Hypotenuse}\; \tan \theta = \dfrac{Opposite}{Adjacent}$

To get you started $\sin 58^{\circ} = \dfrac{4}{c}$ assuming $c$ is the hypotenuse. Now solve for $c$. 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 $180^{\circ}$

EDIT: Fixed some typos.
• Aug 2nd 2010, 01:33 PM
Math 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.

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

But we know x = 4, so

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

Can you find y?

Edit: All angles are in degrees.
• Aug 2nd 2010, 02:44 PM
gabriel
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 PM
Math Major
$tan(58) = \frac{4}{y} \implies y = \frac{4}{tan(58)} =~ 2.5$