GCSE Edexcel Maths Area & Perimeter: ABC and ADC are triangles. The

ABC and ADC are triangles - Edexcel - GCSE Maths - Question 17 - 2017 - Paper 3

Question 17

ABC and ADC are triangles. The area of triangle ADC is 56 m² Work out the length of AB. Give your answer correct to 1 decimal place.

Worked Solution & Example Answer:ABC and ADC are triangles - Edexcel - GCSE Maths - Question 17 - 2017 - Paper 3

Step 1

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Answer

We know that the area of triangle ADC is given by:

ext{Area} = rac{1}{2} imes ext{base} imes ext{height}

Here, the base can be AC, and we know the area is 56 m². We need to find the height corresponding to AC.

To find the height, we can use the angle opposite to AC, which is 105°. So,

ext{height} = AC imes an(105°)

Setting the area equation:

56 = rac{1}{2} imes AC imes (AC imes an(105°))

This gives:

56 = rac{1}{2} imes AC^2 imes an(105°)

Solving for AC, we first need the value of ( an(105°) \approx -0.9657 ):

AC^2 = rac{56 imes 2}{-0.9657}

Calculating gives us AC.

Step 2

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Answer

We can now use the Law of Sines to find AB. In triangle ABC:

rac{AB}{ ext{sin}(48°)} = rac{AC}{ ext{sin}(118°)}

From step 1, we calculated the value of AC. Plugging that into the equation gives:

AB = rac{AC imes ext{sin}(48°)}{ ext{sin}(118°)}

Calculating AB will give us the required length.