Question

Question 7 and the one below it’s Gcse exact trigonometric values

Answer 1

Q. 7.

k = √3/2.

Explanation:

Q. 7.

Consider triangle ABC:

We have sin 30 = y / AC , then 1/2 = y / AC. ( as sin 30 = 1/2).

Therefore AC = 2y.

Consider triangle DCA:-

cos 30 = AC / DA

√3/ 2 = 2y / DA giving DA = 4y / √3

Now look at triangle EDA:

sin 30 = 1/2 = n / (4y / √3)

1/2 = √3n / 4y

4y = 2 √3 n

y = √3 n / 2

So as y = kn then k = √3/2 (answer).

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