8 (a) Write down the exact value of tan 45°
Here is a right-angled triangle:
cos 60° = 0.5
(b) Work out the value of x. - Edexcel - GCSE Maths - Question 9 - 2018 - Paper 1
Question 9
8 (a) Write down the exact value of tan 45°
Here is a right-angled triangle:
cos 60° = 0.5
(b) Work out the value of x.
Worked Solution & Example Answer:8 (a) Write down the exact value of tan 45°
Here is a right-angled triangle:
cos 60° = 0.5
(b) Work out the value of x. - Edexcel - GCSE Maths - Question 9 - 2018 - Paper 1
Step 1
Write down the exact value of tan 45°
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Answer
The exact value of ( \tan 45° ) is 1. This is because in a right-angled triangle, when both the opposite and adjacent sides are of equal length, the tangent, which is the ratio of the opposite side to the adjacent side, equals 1.
Step 2
Work out the value of x.
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Answer
To find the value of ( x ) in the triangle, we can use the cosine ratio, which states that:
[
\cos(60°) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{4}{x}
]
Given that ( \cos 60° = 0.5 ), we can set up the equation:
[
0.5 = \frac{4}{x}
]
Cross-multiplying gives us:
[
0.5x = 4
]
Dividing both sides by 0.5 leads to:
[
x = \frac{4}{0.5} = 8
]
Thus, the value of ( x ) is 8 cm.
