Working in Radians

Uhm maybe a stupid question...

Can you use the formula for an area of a non right-angled triangle using radians...

a= 1/2bh x sin theta

I have noticed I keep getting the same answer for area of triangle and area of sector the triangle is in. Which obviously is not correct - the formula are more or less the same.

Reply 1

DylanJ42

18

Original post by christinajane

Uhm maybe a stupid question...

Can you use the formula for an area of a non right-angled triangle using radians...

a= 1/2bh x sin theta

I have noticed I keep getting the same answer for area of triangle and area of sector the triangle is in. Which obviously is not correct - the formula are more or less the same.

\displaystyle \text{Area of triangle}\: = \frac{1}{2}ab \sin C

C can be in degrees or radians, just make sure your calculator is in the right setting

\displaystyle \text{Area of sector}\: = \frac{1}{2}\theta r^2

so an isoceles triangle with a small angle between the two equal length sides will give roughly the same answer in both formula, although the answers are not usually similar

Edit: could you post an example of a question and your working out

(edited 8 years ago)

Reply 2

Zacken

22

Original post by christinajane

Uhm maybe a stupid question...

Can you use the formula for an area of a non right-angled triangle using radians...

a= 1/2bh x sin theta

I have noticed I keep getting the same answer for area of triangle and area of sector the triangle is in. Which obviously is not correct - the formula are more or less the same.

Do you mean this?

If so, it should work for any triangle. Could you give me an example of your calculation?

Reply 3

christinajane

OP

4

https://0e90d90be05fe2865012661b731d0adbe5865fd8.googledrive.com/host/0B1ZiqBksUHNYT1JhVExXbEs2dk0/C2%20Chapter%2006.pdf

Question three in the mixed exercise - page 46 in the above link.

I may just be reading the question wrong!

The arc formed by a2 is part of the sector?

So area of sector is

A=1/2x17^2 x 2.16
a=120cm

So i worked out the area re of the triangle using the enclosed angle in radians using the formula:

A = 1/2 d x c x sine theta
a= 1/2 17 X 17 X sin 2.16
a = 120

I got the other parts to the question correct so the value for theta is correct.

I got the correct answer in the end using the formula for the segment.

So its more just for information/interest purposes!

I might just be reading the question wrong though....

Reply 4

Zacken

22

Original post by christinajane

A=1/2x17^2 x 2.16
a=120cm

Silly calculation error. :smile:

Try doing that again,

A = \frac{1}{2} \times 17^2 \times 2.16 = \frac{1}{2} \times 289 \times 2.16 = 144.5 \times 2.16 = 312.12 \neq 180

Reply 5

christinajane

OP

4

Argh again!? haha

I think I am dyslexic....no joke!

Thank you Zacken.

Reply 6

Zacken

22

Original post by christinajane

Argh again!? haha

I think I am dyslexic....no joke!

Thank you Zacken.

Not a problem! By the way, when you're replying to someone on here, you should press the "reply" button on their post so that the person receives a notification that you've replied to them! :smile:

Reply 7

christinajane

OP

4

Like this? :smile:

Thank you.

Reply 8

Zacken

22