Question

An observer (O) is located 660 feet from a tree (T). The observer notices a hawk (H) flying at a 35° angle of elevation from his line of sight. How high is the hawk flying over the tree? You must show all work and calculations to receive full credit.

Answer 1

@ganeshie8

Answer 2

@amistre64

Answer 3

@phi

Answer 4

Help me

Answer 5

So obviously we need to keep on using trignometric ratios

Answer 6

First, identify what sides and angles you know. and the side you do not know.

using the angle you know, define the sides (opposite and adjacent depends on which angle you are using)

can you do that ?

Answer 7

Umm im not very good at this but the 35 degree angle should be the adjacent and the 660 should be the hypotenuse and leaving us with the oppsite being unknown am I correct ? :/

Answer 8

the angles do not have names.

we pick one of the 2 angles (not the 90 angle)
we then name the sides. There are 3 sides. One side (the longest side, and the side opposite the 90 degree angle is always the hypotenuse)

Answer 9

ok

Answer 10

there are two sides left to name.

Put your finger on the angle we are going to use.
the SIDE opposite that angle is labeled opposite
the SIDE that makes up the angle is the adjacent side

Answer 11

OK

Answer 12

there is only one angle (besides the 90 angle) that we know.
It is the 35 degree angle at O
what side is the opposite side ?
what side is the adjacent side ?

Answer 13

Adjacent is the side with the degree correct and the opposite side is the side opposite to the adjacent side

Answer 14

If you label your picture it should look like this

Answer 15

ok

Answer 16

If we switched to the other angle, we would have to change which side is labeled opposite and which is adjacent.

But we are not going to do that .

Answer 17

now, of the 3 sides, which 2 are we going to use?

one should be the one we are "solving for"
one should be where we know its length.

which 2 sides are we going to use?

Answer 18

all the sides have names, so you should know the names of the 2 sides we will use.

Answer 19

Umm im not sure. Would it be adjacent and hypotenuse

Answer 20

one should be the one we are "solving for"

what side are we looking for so we can answer
How high is the hawk flying over the tree?

Answer 21

35 degrees

Answer 22

which is the hypotenuse

Answer 23

35 degrees is the measure of an angle.
we want the name of a side.

which side represents the height of the hawk above the ground ?

Answer 24

The adjacent side

Answer 25

Ok, you are saying the height of the hawk is this distance

Answer 26

yes

Answer 27

the purple line from O to T is on the ground.
The hawk is at position H in the figure.

Answer 28

I think the height is the line from T to H

Answer 29

like this

Answer 30

that height of the hawk is the "opposite side"

next, pick a side that we know. which side's length do we know?

Answer 31

Not sure will it be hypotenuse

Answer 32

@phi

Answer 33

@amistre64 @ganeshie8

Answer 34

plzzz all i want is to finsih

Answer 35

are any of the sides labeled with a distance ?

Answer 36

the adjacent ahgle has 660

Answer 37

yes, so we should use that side.

we want to know the opposite side
we know the adjacent side

which of SOH CAH TOA
should we use?

Answer 38

Tan

Answer 39

or toa

Answer 40

yes

that means you should write
tan 35 = ?

Answer 41

Tan 35 = opposite side / 660

Answer 42

to keep it easier to type, call the opposite side "h"
Tan 35= h/660
to solve for h, multiply both sides by 660
660 * Tan 35 = h

now you need a calculator.

Answer 43

312.717715474

Answer 44

@phi

Answer 45

what did you get for tan 35 ?

Answer 46

0.47381472041

Answer 47

your calculator is in radian mode.
you should change to degree mode.

Answer 48

Oh Ok

Answer 49

0.70020753821

Answer 50

now multiple by 660 for the answer

Answer 51

Ok thanks u soooooo much