Question

Find the length of side b to two decimal places

Answer 1

You know the length of the hypoteneuse and you know the angle between the hypoteneuse and the base. How can you find the length of the other sides with those two things?

Answer 2

i know a²+b²=c² but i dont know how that is relevant in this problem
thats the information i was given to solve this

Answer 3

Please use sine rule.

Answer 4

\[\sin\theta = b / h\] where \(h\) is the hypotenuse (which we know to be 25) and \(\theta\) is the angle (which we know to be 35 degrees).

Answer 5

Close. The hypoteneuse multiplied by the sine of the angle will give you the side opposite the angle and the hypoteneuse multiplied by the cosine of the angle will give you the side adjacent to the angle

Answer 6

that was @erin512 just fyi

Answer 7

what was me?

Answer 8

my last comment

Answer 9

@azolotor's comment was directed at you, I hope, because mine isn't close, it's a different word that starts with c :-)

Answer 10

oh im sorry

Answer 11

how would i find the answer from there?

Answer 12

Do you have a calculator?

Answer 13

yes

Answer 14

Okay, make sure it is set to do trig functions with degrees, then take the sin of 35 degrees. Multiply that by the length of the hypotenuse to get the side opposite the angle. Round to the appropriate number of places.

Answer 15

i got 13.34

Answer 16

Some people find the mnemonic SOHCAHTOA useful for remembering this.

Sin = Opposite over Hypotenuse
Cos = Adjacent over Hypotenuse
Tan = Opposite over Adjacent

Answer 17

i mean 14.34 sorry

Answer 18

oh i've heard that before

Answer 19

Looks good to me!

Answer 20

would that be the answer?

Answer 21

14.34?

Answer 22

Hmm, where'd my drawing go? :-(

Yes, 14.34 is the answer.

Answer 23

thank you so much! you were both a big help!

Answer 24

do you know how i could find the length of side a?

Answer 25

The way I remember it is by the unit circle - the x-axis is the cos value, the y-axis is the sin value, and I just remember that cos (0) = 1.

Answer 26

the same way as i found this one?

Answer 27

Yes, I do. Look at SOHCAHTOA and see if you can figure it out.

Answer 28

I'm not sure how to determine which one to use

Answer 29

I know that you used SOH to find b but I'm not sure why

Answer 30

Well, you're trying to find the adjacent side, right?

Answer 31

As you already know the opposite side and the hypotenuse, you have a choice of two ways to proceed.

Answer 32

Sorry, 3 if you count Pythagoras

Answer 33

the adjacent side to what?

Answer 34

I used SOH because I knew the angle (and thus the sin of the angle) and the hypotenuse, and was trying to find the opposite side. S, H, and O respectively

Answer 35

Adjacent to the angle

Answer 36

oh ok

Answer 37

So, you are trying to find the Adjacent side, you know the angle, and you know the hypotenuse. What does that suggest you might use?

Answer 38

Cos?

Answer 39

Ding ding ding! We have a winner!

Answer 40

Another possible correct answer would be tan, because we know the angle, and we know the opposite. TOA -> \(\tan \theta = b/a\) or \( a = b / \tan \theta\)

Answer 41

At this point, we could also use Pythagoras, as we know two of the sides of a right triangle:
\[25^2 = a^2 + b^2\] (and we know \(b\) from our earlier calculation).

Answer 42

What do you get for the length of side a? Quickly, I have to leave :-)

Answer 43

419.37

Answer 44

correct?

Answer 45

whoops i forgot to take the square. so it would be 209.69

Answer 46

Come on....1 side of the triangle is 25, another side is about 14, and the third side is going to be 209?!?

Answer 47

If you did it with cos, cos (35) = 0.819... 25*0.819 = 20.48

If you did it with tan, tan (35) = 0.700, 14.34/0.700 = 20.48

If you did it with Pythagoras, 25^2 = 14.34^2 + a^2, a = sqrt(625-205.64) = 20.48

Answer 48

i didn't think it made sense but when i used pythagoras i did it wrong. i see much better now. thank you so much again