Sine, Cosine Rule & Area of Triangles

Calculate the length of .
Give your answer correct to 3 significant figures.

The diagram shows parallelogram .

Work out the area of the parallelogram.
Give your answer correct to 3 significant figures.

.......................

Work out the length of the diagonal of the parallelogram.
Give your answer correct to 3 significant figures.

.....................

The diagram shows triangle .

Calculate the length of .
Give your answer correct to 3 significant figures.

.........................

A triangle has sides of length 8 cm, 10 cm and 14 cm.

Work out the size of the largest angle of the triangle.
Give your answer correct to 1 decimal place.

Here is a triangle.

Circle the correct equation.

Here is a triangle.

Leah tries to use the sine rule to work out the size of angle .
Here are the first two lines of her working.

What error has she made in this working?

Work out the size of angle .

...............................degrees

A ship sails from to and then from to .

is 12 miles from , on a bearing of 080°

is 28 miles from , on a bearing of 155°

Work out the direct distance from to .

and are triangles.

The area of is 80.5 cm²

Work out the area of .
Give your answer to 3 significant figures.

...............................cm²

Liz and Tia are walking towards a shop along different straight paths.

The diagram shows their positions at 2 pm

Assume they walk at the same speed.

Who will arrive at the shop first?
You must show your working.

In fact, Liz walks at a faster speed than Tia.

How does this affect the answer to part (a)?

Here is a triangle.

Work out the length 

.................cm

In the triangle, angle is obtuse.

Work out the size of angle .

...................degrees

The diagram shows a triangular field PQR which is used to grow organic carrots.

PQ = 100 m, PR = 80 m and angle RPQ = 30°.

In recent years, an average of 2.5 kg of carrots has been harvested from each square metre of  the field.

Use this information to work out the total mass of carrots that might have been harvested from the field in 2019.

......................................................kg

Why might the answer to partbe unreliable?

ABC and ACD are triangles.

Show that AC = 13.0 cm, correct to 3 significant figures.

Calculate BC.

..................... cm

Calculate length DF in this triangle.

..................................................... cm

Calculate angle ACB in this triangle.

T is a radar tower.
A and B are two aircraft.
At 3pm

• aircraft A is 3250km from T on a bearing of 015°
• aircraft B is 4960km from T on a bearing of 057°.

Calculate the distance that was between aircraft A and aircraft B at 3pm.

....................................................... km

and are triangles.

The area of triangle is 56 m²

Work out the length of
Give your answer correct to 1 decimal place.

is a parallelogram.

= 9 cm
 = 11 cm
Angle = 100°

Calculate the area of the parallelogram.
Give your answer correct to 3 significant figures.

is an acute-angled triangle.
= 7cm
 = 8cm

The area of triangle is 18 cm².

Work out the size of angle .
Give your answer correct to 3 significant figures.
You must show all your working.

The diagram shows a hexagon .

and are congruent parallelograms where 
is the point on and  is the point on such that 

Given that angle 

prove that  

is an acute angled triangle.

The area of triangle is 19 cm².

Work out the size of angle .
Give your answer correct to 3 significant figures.

is a triangle.
is a point on .

Work out the area of triangle .
Give your answer correct to 3 significant figures.

The diagram shows triangle

Given that angle is obtuse, work out the area of triangle .
Give your answer correct to 3 significant figures.

The diagram shows triangle

correct to one decimal place
     correct to the nearest whole number
   correct to the nearest whole number

Calculate the upper bound for the value of
Show your working clearly.
Give your answer correct to 3 significant figures.

is a quadrilateral where and are points on a circle.



Angle
Angle

Work out the perimeter of quadrilateral .
Give your answer correct to one decimal place.

....................................................... cm

Here is a triangle .

The perimeter of the triangle is .

Given that 
find the value of .
Show your working clearly.

The diagram shows a regular octagon 

Each side of the octagon has length 

Find the area of the shaded region 
Give your answer correct to the nearest 

.............................................  

In this question, all lengths are in centimetres.

is a point on a circle, centre .
is a point on a different circle, centre .

The equation of the larger circle is    

radius of smaller circle : radius of larger circle   = 4 : 5

Work out the size of angle

............................................ degrees

The area of this triangle is 

Work out the value of .
Give your answer in the form  where  and  are integers greater than 1.

The diagram shows a logo.

and are congruent triangles.
is a sector of a circle, centre .

Show that the area of the logo is 510 cm² to 2 significant figures.