AS Level Maths Edexcel Trig Help URGENT

Alright so I have this question and I want to see how others have answered it.

The diagram shows triangle ABC with AC=8x-3, BC=4x-1, angle ABC=120 degrees and angle ACB=15 degrees.

(a) Show that the exact value of x is 9+√6/20 (7 marks)
(b) Find the area of triangle ABC giving your answer to 2 decimal places
(3 marks)

Reply 1

username3085646

OP

11

I don't mind anyone answering it please. This question has been bugging me for so long

Reply 2

Y2_UniMaths

19

What have you been able to do so far?

Reply 3

username3085646

OP

11

Not much other than find the other remaining angle. I'm unsure as to how I should start it

Reply 4

brainmaster

14

I'm seeing the first part u use the sine rule or cosine rule and then u simplify to make ur answer look like What They want then second one u just use replace the value of x in the equation for the length is AB and BC and then use the angle ACB and get the area using 1/2ab sinc
let me know if this helped😊

Reply 5

brainmaster

14

Original post by bluepotato

Alright so I have this question and I want to see how others have answered it.

The diagram shows triangle ABC with AC=8x-3, BC=4x-1, angle ABC=120 degrees and angle ACB=15 degrees.

(a) Show that the exact value of x is 9+√6/20 (7 marks)
(b) Find the area of triangle ABC giving your answer to 2 decimal places
(3 marks)

actually get the missing angle and then use sine rule and make sure u use the exact value of sin 45 and sin 120 to get to the answer they require u to get...

Reply 6

username3085646

OP

11

Original post by brainmaster

I'm seeing the first part u use the sine rule or cosine rule and then u simplify to make ur answer look like What They want then second one u just use replace the value of x in the equation for the length is AB and BC and then use the angle ACB and get the area using 1/2ab sinc
let me know if this helped😊

Could you do the question so I can see? We recently had this question in a test and I have to review it again after my teacher has marked it.

Reply 7

chailatte2407

5

Original post by bluepotato

Could you do the question so I can see? We recently had this question in a test and I have to review it again after my teacher has marked it.

OK so you know two of the side lengths and all three of the angles (using the fact that the sum of the angles in a triangle must be 180 degrees).

So you need to put the information you have into the sine rule (i.e. sinA/A = sinB/B = sinC/C. This rule relies upon knowing pairs of angles and the lengths of their opposite sides. So the 120 degree angle is opposite the side of length (8x-3) and the 45 degree angle is opposite the length of side (4x-1). So now you have to work through the algebra of that. Remember that sin(180 - x) = sin(x) if you're not allowed a calculator!

The area of a triangle can be written as (1/2)*absinC so in this case that would be (1/2)*(4x-1)*(8x-3)*sin(15)

Reply 8

username3085646

OP

11

Original post by chailatte2407

OK so you know two of the side lengths and all three of the angles (using the fact that the sum of the angles in a triangle must be 180 degrees).

So you need to put the information you have into the sine rule (i.e. sinA/A = sinB/B = sinC/C. This rule relies upon knowing pairs of angles and the lengths of their opposite sides. So the 120 degree angle is opposite the side of length (8x-3) and the 45 degree angle is opposite the length of side (4x-1). So now you have to work through the algebra of that. Remember that sin(180 - x) = sin(x) if you're not allowed a calculator!

The area of a triangle can be written as (1/2)*absinC so in this case that would be (1/2)*(4x-1)*(8x-3)*sin(15)

Omds thanks so much!! I'll do it and try it out.

Reply 9

desert_fairy

16

Original post by chailatte2407

OK so you know two of the side lengths and all three of the angles (using the fact that the sum of the angles in a triangle must be 180 degrees).

So you need to put the information you have into the sine rule (i.e. sinA/A = sinB/B = sinC/C. Thdidis rule relies upon knowing pairs of angles and the lengths of their opposite sides. So the 120 degree angle is opposite the side of length (8x-3) and the 45 degree angle is opposite the length of side (4x-1). So now you have to work through the algebra of that. Remember that sin(180 - x) = sin(x) if you're not allowed a calculator!

The area of a triangle can be written as (1/2)*absinC so in this case that would be (1/2)*(4x-1)*(8x-3)*sin(15)

did you get 0.26 for the area? it seems a bit small

Reply 10

jacqueslaflame

14

Original post by desert_fairy

did you get 0.26 for the area? it seems a bit small

i was doing this question just now and came on here to check because i got that too but i also thought it was too small

if we both got it i'm assuming we've done it fine though?