# right triangle trig cont. w/ questions

#### gabriel

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

#### lvleph

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.

#### 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.

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.

lvleph

#### 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?

#### Math Major

$$\displaystyle tan(58) = \frac{4}{y} \implies y = \frac{4}{tan(58)} =~ 2.5$$

gabriel
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