Trigonometry! #108

Geometry Level 2

The top of a broken tree has its top end touching the ground at a distance of $15m$ from the bottom. The angle made by the broken end with the ground is $30^{\circ}$ . Then find the length of the broken part.

Express your answer in the form of $a\sqrt{b}m$ , where $a$ and $b$ are coprime positive integers. Enter the value of $a+b$ .

This problem is part of the set Trigonometry .

The answer is 13.

1 solution

Michael Fuller
Apr 23, 2015

The broken tree forms a right triangle, and the length we are asked to work out is the hypotenuse of this triangle.

Let the vertical leg of the triangle be $x$ . Using the sine rule: $\frac { 15 }{ \sin { 60 } } =\frac { x }{ \sin { 30 } } \\ \Rightarrow x=5\sqrt { 3 }$

The hypotenuse can now be found with Pythagoras: $\sqrt { { \left( 5\sqrt { 3 } \right) }^{ 2 }+{ \left( 15 \right) }^{ 2 } } \\ =10\sqrt { 3 }$

$10+3=\boxed { 13 }$ .

And my graphic design skills are still as bad as ever.

Trigonometry! #108

The answer is 13.

1 solution

0 pending reports