Question

In the diagram below, BC is an altitude of ABD. To the nearest whole unit, what is the length of CD?

Answer 1

23 for apex

Explanation:

Answer 2

We will start with the triangle ABCm with AC = 44 and BC = 32

We work out the angle BAC, labelled as x° in the diagram shown below

Using the trigonometry ratio, we have


`tan(x)= (opposite)/(adjacent)`

`tan(x)= (32)/(44)`

`x= tan^(-1) ((32)/(44))`

`x=36`° (rounded to the nearest integer)

Then we work out the size of angle y°, shown in the diagram below.

By using the angles in a triangle rule, we have
y°=180°-(90°+36°)= 54°

Then we use this information to work out the length of CD


`tan (y)= (BC)/(CD)`

`tan(54)= (32)/(CD)`

`CD= (32)/(tan(54))`

`CD=23` (to the nearest integer)