Question

Find the value of x in each figure

Answer 1

Explanation:

b. It is a right angle triangle with 2 sides given we are to use Pythagoras theorem.

`{65}^(2) = {25 }^(2) + {x}^(2)`

`4225 = 625 + {x}^(2) \\{x}^(2) = 4225 - 625 \\ {x}^(2) = 3600 \\ x = 60`

c. Here 2 angles and one side is given. So we use sine rule

`sin(90) / 50 = \sin(60) / x \\ x \sin(90) = 50 \sin(60) \\ x = 25 √(3) \\ x = 43.3`

Note: sin 90 is 1

sin 60 is √3 /2

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a. since the x is the same we would use sin rule

`\sin(45) / x = \sin(90) / 16 \\ x = 16 \sin(45) \\ x = 16 * √(2) / 2 \\ x = 8 √(2)`

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