Question

609 4 What is the length of u and vin this 30-60-90 A triangle? U = 16 v = 8 U = 8v = 473 U = 473 V = 8 U = 42 y = 8

Answer 1

`\begin{gathered} u\text{ = 8} \\ \\ v\text{ = 4}\sqrt[]{3} \end{gathered}`

For a 30-60-90 triangle, we have a fixed ratio for the length of the sides of the triangle

These lengths are in the ratio;

`1\text{ : }\sqrt[]{3}\text{ : 2}`

Since u faces the right angle, it has the longest length, followed by v which faces the angle 60

The lengths are thus;

`\begin{gathered} u\text{ = 4 }*\text{ 2 = 8} \\ v\text{ = 4 }*\text{ }\sqrt[]{3}\text{ = 4}\sqrt[]{3} \end{gathered}`