Question

Find the altitude of an isosceles triangle with a vertex angle (that is, the non-base angle) of 70° and a base of 246. Draw a diagram and find the length of the altitude.

175.7
81.6
89.5

Answer 1

Hello @Elizabeth2001 !

The key point of this problem is that this triangle is an isosceles triangle
this means that the base angles and two sides of the triangle are of equal length

Answer 2

Now, we are given that the vertex angle is 70 degrees
and that the base of this triangle is 246 units

Answer 3

A really interesting property of an isosceles triangle is that the altitude from the vertex angle is also the angle bisector of the angle. It also is the perpendicular bisector of the triangle

so we get:

Answer 4

Thanks a lot for helping me

Answer 5

The next step would involve the tan(x) = opposite/adjacent
have you learned this?

Answer 6

I have learned this I just wanted to see if I had the right answer

Answer 7

Sure, what answer did you get? :)

Answer 8

I believe I got 86.1

Answer 9

You almost got the right idea!



if tan(33) = opposite / adjacent

then
adjacent * tan(33) = opposite
and
adjacent = opposite / (tan(33))

Answer 10

In other words,
you should try:

123 / tan(33)

Answer 11

*I mean 35 for both cases, sorry

Answer 12

Ok you seem pretty cool

Answer 13

Thanks :)

I pretty sure 123 / tan(35) can get you to the answer you need
if you need anymore help, feel free to ask another question or tag me with @Angle to summon me :P

Answer 14

You’re welcome 😌
And ok
I don’t want to come off to awkward but do you want to email each other

Answer 15

I don't check my email all that much, we have a messaging system here (click on my name and you can send a message) we also have a chat (at the bottom of the screen).

If you're looking to get more help in the future, this website is the best place to keep asking (instead of emailing me); we have great math people online most of the time :)

Answer 16

Ok ☺️☺️