#How to find the height with 2 lengths and 2 angles?

43 messages · Page 1 of 1 (latest)

vagrant pebble
#

. A person observes the top of a tower from two points on the ground. From the first point, 30 m from the base, the angle of elevation is 30∘. From a second point, 50 m from the base (further away), the angle of elevation is 20∘. Find the height of the tower.

I gave this a try, I drew the triangle, the 2 lengths and angles pointing towards the top of the tower. I used tangent to find the opposite/height for both triangles, but they dont equal the same thing?

Im confused on if theres another way to find the height that I wasnt taught? We've only been taught sohcahtoa so far and i dont know what im doing wrong (I also checked yt and google for examples similar but cant find a similar question to this)

blazing templeBOT
sudden forge
chilly ore
#

this sounds like a case of similar triangles, but yeah do send your diagram OP

vagrant pebble
vagrant pebble
#

(The tan50 is me adding the 2 seeing if I would find the height, sadly to no avail)

chilly ore
#

so you solved it with similar triangles?

vagrant pebble
#

What’s that

chilly ore
#

your two triangles share a side, has the ground sides proportional to each other (because they're both on the ground), and share an included angle (the angle between the tower and the ground)

#

ok maybe not similar triangles, but you can definitely use proportion to kill this

vagrant pebble
#

Any videos to watch about said “proportions”

chilly ore
#

wait let me see what info you have

vagrant pebble
#

Okay!

chilly ore
#

oh ok I see it now

#

you are not mistaken

vagrant pebble
#

Okay I’m ready!

chilly ore
#

this is a faulty question

vagrant pebble
#

RIGHT?

chilly ore
#

and I completely agree with your calculations

vagrant pebble
#

you know what’s so funny is there’s another question exactly like this

chilly ore
#

just as faulty?

vagrant pebble
#

Yes

#

I even asked a tutor this question and they said the same

#

I asked chatgpt and it somehow found the answer but idk how, but even the robot had a moment where it spoke to itself

#

Something like “oh wait no that’s not right, I gotta do blablablabla?”

chilly ore
#

4o does that a lot

#

5 also does that but less frequently, though 5 Thinking is fine

vagrant pebble
#

I asked 5

#

😭

chilly ore
#

then again, I don't recommend relying on GPT always

vagrant pebble
#

Yea I prefer to ask humans anyways

#

Those dang klankers (I love this new robotic derogatory word)

#

😭😭😭😭😭😭😭😭😭

chilly ore
#

LOL

#

anyway, anything else?

vagrant pebble
#

No nothing else for now! Thank you so much for your help :))

#

I will close this now!

chilly ore
#

aight, see you around!

vagrant pebble
#

See you!

#

.close