Trig Function Help: How to Solve Two Problems Involving Angles and Measurements

[lorelyi328]

I have two problems that I'm not sure how to work out.

1. You are driving to st louis, missouri and in the distance you see the gateway-to-the-west arch. this monument rises 192 m. you estimated your line of site to the top of the arch to be 2 degrees above horizontal. how far approximately (in km) are you from the base of the arch ?

OKay so i have the angle opening up to the right at 2 degrees, and the height of the leg in the opposite postion as 192 m. i tried to use sin 2 degrees * 192 meters = 6.70 m. i know that this is wrong already since in km, this number would be a lot smaller. the answer in the back of the book is 5.5km. I'm not sure what I'm doing wrong. i tried again, to use tan since it would be opposite, and it's the adjacent leg that i can't find. i get the same answer.

2. the silhouette of a christmas tree is an isoceles triangle. the angle at the top of the tree is 30.0 degrees, and the base measures 2.00 m across. How tall is the tree.

i tried a couple of things with this. first i tried the sin of 30 degrees * 2m and i know that the answer can't possibly be 1m. then i thought to maybe try tan since it is the adjacent leg i would be trying to get. the answer isn't 1.15 either. finally i tried to get the other angles at the bottom of the isoceles triangle as 75 degrees since triangles = 180 degrees, the top is 30 degrees, and the bottom two have to be equal. so then i tried the cos of 75 degress * 2 m and this didn't work either. the answer in the back of the book is 3.73m. thanks for the help.

 

[Integral]

You are given the height and the opposite that height. you need to find length of the edge adjacent to the angle. What trig function involves those sides of a right triangle?

Remember that when applying trig you have to work with right triangles. Cut the trees isosceles triangle in half from the peak to the midpoint of the base, you now have 2 similar right triangles. Consider the resulting angle and and given side. Determine the side of the right triangle you need to find. Use the trig function which is defined by those sides.

 

[lorelyi328]

okay, the tree problem, i totally understand now. i did get the answer. i had forgotten that you could split triangles up like that. the other problem I'm totally stumped on still. okay, with the height as the opp and the adjancet leg needed you would need to use tangent. i realized that i had set the problem up wrong. i was dividing by the 192 m. i should have been dividing the 192 m by the tan of 2 degrees. i was writing it down like an algebra equation when i did it otherwise i would have realized my mistake. thanks ! it's been a long time for me with algebra, geometry, and trig. you really need them a lot for physics.

should i specify that this is just studying I'm doing for myself ? this actually aren't my homework questions. I'm using the questions in the book to help me study. i have a ten chapter test to study for on monday. i already have gone through chapters 1-4 but am going back over them again. I've really come to find that everytime i go back over the chapters, i find new stuff that i didn't know about before. hmmmm. however I'm really starting to get a better understanding for it. thanks again.