AS maths paper help

A parallelogram PQRS has area 50cm²
Given:
- PQ has length 14cm
- QR has length 7cm
- angle SPQ is obtuse
find:
a) the size of angle SPQ, in degrees, to 2 decimal places
b) the length of the diagonal SQ, in cm, to one decimal place

Reply 1

Pangol

15

Original post by boxycox

A parallelogram PQRS has area 50cm²
Given:
- PQ has length 14cm
- QR has length 7cm
- angle SPQ is obtuse
find:
a) the size of angle SPQ, in degrees, to 2 decimal places
b) the length of the diagonal SQ, in cm, to one decimal place

I'd start by drawing a sketch, and then add a line joining Q and S. Then think about triangle PQS only. You can easily see what the area of this triangle is, and there is only one simple formula you know for the area of a triangle - that should do the first part for you. The second part is then easy.

Reply 2

boxycox

OP

2

Original post by Pangol

I'd start by drawing a sketch, and then add a line joining Q and S. Then think about triangle PQS only. You can easily see what the area of this triangle is, and there is only one simple formula you know for the area of a triangle - that should do the first part for you. The second part is then easy.

Yeah, I found that angle to be 30.6 degrees. It was the obtuse part that I don't understand.

Reply 3

Pangol

15

Original post by boxycox

Yeah, I found that angle to be 30.6 degrees. It was the obtuse part that I don't understand.

Considering they tell you it is obtuse, that clearly is not the angle you're after. But you have obviously got as far as sin(SPQ) = 25/49. You need to remember that there is more than one answer to this, and the one that your calculator gives you is not the one you want.

Reply 4

SvhwiaishebSee

2

Where did you find this question from, which question paper

Reply 5

allan.turing15

4

You minus the 30.68 from 180 to give the obtuse angle which so the answer for (a) is 149.32

For B you make a line from the diagram and then you use the cosine rule the angle would be 30.7 and the 2 lengths of the triangle will be 14 and 7.

Reply 6

lydia5

1

where did you get the paper from ??
please ASAP

(edited 2 years ago)

Reply 7

Nayel

4

It is the 2110 8MA0-01 AS Pure Mathematics – October 2021 paper

Reply 8

dogbo

1

would the answer to B be 20.3cm or 8.7cm? as you said use 30.68 as angle but wouldn’t the obtuse calculated be used instead?

Reply 9

AkhtarK

1

1) start by drawing a parallelogram.
2) label points from p-s

PQ is 14cm, QR is 7cm, so this must match on both sides.

Then use 0.5absinC and equate to 25 as half of area
So 14x7SinC = 50
SinC = 50/98
C = arcsin 50/98
= 30.68.

Use 180-ans to get obtuse angle = 149.3 degrees

Original post by boxycox

A parallelogram PQRS has area 50cm²
Given:
- PQ has length 14cm
- QR has length 7cm
- angle SPQ is obtuse
find:
a) the size of angle SPQ, in degrees, to 2 decimal places
b) the length of the diagonal SQ, in cm, to one decimal place