Two challenging (or not?) Maths GCSE problems - hoping you can do them tonight???

[loveyouradvice]

Hi... DD working through "Michael Gove's" papers as she calls them and has come across two things to calculate that they haven't covered and she can't find in her Maths books.... I've had a look and I can't either! She's an Add Maths student so is convinced she should be able to work it out and is missing something obvious....

So hoping someone can tell us HOW to do one or both of these?

1. The area of a kite to 3 significant figures. Two adjacent sides are 6.4 cm and 9.7 cm and the angle between them is 110 degrees. That's it... in a diagram obviously!
   

1. A quadrilateral:
   

Corners are M - N - P - L
Asks for size of angle of MLP to 3 signify figures
Info given (in diagram) is:
LMN: 58 degrees
NPL 72 degrees
PNM not given
SIdes: MN 13.7 cm, NP 4.3 cm, PL 15.6 cm

Huge thanks and think Ill be kicking myself when someone tells me ... ages ago I did Maths A level.....

[StealthPolarBear]

Well the first one needs pythagoras in simultaneous equations I thiibk
Those lengths are the hypotenuse of the two triangles that make up one half of the kite

[MsAwesomeDragon]

1. Cut it into 2 triangles and work out the area of each using 1/2 ab sinC

[StealthPolarBear]

A2+b2=c2
D2+b2=f2

Where c and f are the two lengths given

Can then find a relationship between a band d and work in some geometry with that angle

[MsAwesomeDragon]

1. Use cosine rule to work out the length LN.
   

Then use sine rule to work out PLN, and sine rule again to work out MLN.
Add them together to make MLP

[ThePrincipal]

1

Use the sin formula for calculating the area of the triangle described.
Then double it for the area of the kite.

Area of triangle = 1/2 (a b sin C)

iirc without looking it up

[MsAwesomeDragon]

In question 1, you need to remember that a kite is symmetrical so you can split it into 2 congruent triangles. And use the formula area =1/2 a b sinC

[loveyouradvice]

Fab thanks.... much appreciated!