Kim is watching a fireworks display from an observation spot 5 miles away. Find the angle of elevation from Kim to the fireworks, which are at a height of 0.3 miles.

Answer 1

Fireworks!!!!

|

| 0.3 miles

|

|

90_________________θ Kim

5 miles

Hi Evelyn!

Excuse my crude picture but it's the best I have here! So I named the angle of elevation between Kim and the fireworks θ (theta) as you can see in the picture. Since this set up forms a right triangle we can use right triangle trig ratios to solve for θ!

Remember the ratio of the opposite side of an angle in a right triangle to its adjacent side is represented by the tangent function. tan θ = o/a. Here we have:

tan θ = 0.3/5

tan θ = .06

tan^-1(tan θ) = tan^-1(.06) - since our unknown is the angle Θ take the inverse tangent (tan^-1) of both sides.

θ ≈ 3.43°

Hope this helps!

Answer 2

This problem can be diagrammed as a right triangle (not to scale)

fireworks

0.3 |\

| \

| \

| \

| \

| \

| \

| E \

|---------- Kim

5

The angle of elevation can be determined using a trig function.

Relative to the angle of elevation (E) we have the lengths of the opposite side (0.3) and the adjacent side (5). This means we can use the tangent function which equals opposite side/adjacent side.

tan(E) = 0.3/5 = 0.06

so E would be arctan(0.06) = 3.43 degrees

Answer 3

Hello Evelyn!

If you draw this situation, you'll see that it forms a right triangle with one cathetus measuring 5 miles and the other measuring 0.3 miles.

So you need to find an angle whose tangent is 0.3/5 = 0.06 = 3.43°

If you need a class, feel free to message. Best wishes!