Trig Function Help

[ShannonR.]

A monument is 116 m high and casts a shadow of 196 m. What is the angle of the elevation of the sun?

So far I drew the right traingle and labeled 116 m as the adjacent side. 196 as the opposite side and up in the top corner is the theta?
In my class we use SOH-CAH-TOA, And I'm unsure which to use or what to type into the calculator. My teacher talks about cross multiplying things.

Besides this problem, I am so lost on this subject. How do you know which function to use for a problem?

 

[wjm11]

A monument is 116 m high and casts a shadow of 196 m. What is the angle of the elevation of the sun?

So far I drew the right traingle and labeled 116 m as the adjacent side. 196 as the opposite side and up in the top corner is the theta?
In my class we use SOH-CAH-TOA, And I'm unsure which to use or what to type into the calculator. My teacher talks about cross multiplying things.

Besides this problem, I am so lost on this subject. How do you know which function to use for a problem?

We measure the angle of elevation of the sun from the horizon upwards, so let’s let the angle on the ground (at the bottom of your triangle) be theta.

Now, looking from the corner where theta is, we would call the vertical side (the height of the monument, 116m) the “opposite side,” and the shadow on the ground (196m) is the “adjacent side.” (The terms “adjacent” and “opposite” depend on which corner of the triangle we are looking from.)

Now we must decide which trig formula to use. It’s simple: we have info on the adjacent side and on the opposite side, so we use a formula that has those two things in it, TOA. So,

Tan (theta) = Opp./adj. = 116/196

Since we need to solve for the angle, we need to use the “arctan” (or tan to the –1 power) on the calculator:

Arctan(tan(theta)) = arctan(116/196)
Theta = 30.62 degrees

Make sense?

 

[ShannonR.]

yes thank you so much. Now I need to do the rest of my homework. Oh greatt. :/