GCSE Edexcel Maths Right-Angled Triangles - Pythagoras & Trigonometry: 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

To find the length of CD, we can use the formula for the area of a triangle:

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

We know the area of triangle ADC is 56 m² and angle ADC is 105°. The height from A to line CD can be calculated as:

Calculate the height (h) using: $ext{Area} = rac{1}{2} imes CD imes h$ $56 = rac{1}{2} imes CD imes h$ We will calculate CD first.

Step 2

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Answer

Using the sine rule, we have:

$rac{CD}{ ext{sin}(A)} = rac{11}{ ext{sin}(105°)}$

Here, A is the angle opposite to side CD, which is 48°.

Thus, substituting the sine values gives us:

$CD = 11 imes rac{ ext{sin}(48°)}{ ext{sin}(105°)}$

Calculating the value yields approximately:

$CD ≈ 8.2 m$

Step 3

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Answer

From the triangle ABC, we can use the sine rule again to find AB:

$rac{AB}{ ext{sin}(B)} = rac{CD}{ ext{sin}(C)}$

Substituting the known values:

$rac{AB}{ ext{sin}(118°)} = rac{8.2}{ ext{sin}(48°)}$

This gives us:

$AB = 8.2 imes rac{ ext{sin}(118°)}{ ext{sin}(48°)}$

Upon calculating, we get:

$AB ≈ 10.4 m$