Question

I have to find the unknowns in the graph below and I need to quote my answer to 4 significant figures. Can anyone help me?

Answer 1

`x = 36.87`
`y = 3`
`z = 5`

Explanation:

To find `x`, we use the fact that the sum of the inner angles of a triangle is `180°`. Since the two known angle sum up to `90+53.13 = 143.13`, `x` will be the remaning angle to reach `180`, i.e.

`x = 180 - 143.13 = 36.87`

For `z` we may use the theorem that states that

`\frac{4}{\sin(53.13)} = \frac{z}{\sin(90)}`

and thus

`z = \frac{4}{\sin(53.13)} = 5`

For `y` we can simply use the Pythagorean theorem: we look for a leg and we have the hypotenuse and the other leg, so:

`y = \sqrt{5^2-4^2} = \sqrt{25-16} = \sqrt{9} = 3`