Answer:
[tex]AD = 403.75[/tex]
[tex]CD = 115.70[/tex]
[tex]BD = 294.93[/tex]
Step-by-step explanation:
Given
The above triangle
Solving (a): AD
To solve AD, we consider triangle ACD.
Using cosine formula:
[tex]cos(\angle A) = \frac{AD}{AC}[/tex]
Where:
[tex]\angle A =16[/tex]
[tex]AC = 420[/tex]
So:
[tex]cos(16) = \frac{AD}{420}[/tex]
[tex]AD = 420 * cos16[/tex]
[tex]AD = 420 * 0.9613[/tex]
[tex]AD = 403.75[/tex]
Solving (b): CD
Here, we make use of Pythagoras theorem:
[tex]AC^2 = AD^2 + CD^2[/tex]
So:
[tex]420^2 = 403.75^2 + CD^2[/tex]
[tex]176400 = 163014.0625 + CD^2[/tex]
[tex]CD^2 = 176400 - 163014.0625[/tex]
[tex]CD^2 = 13385.9375[/tex]
[tex]CD = \sqrt {13385.9375[/tex]
[tex]CD = 115.70[/tex]
Solving (c): BD
Here, we make use of Pythagoras theorem:
[tex]AB^2 = AD^2 + BD^2[/tex]
[tex]BD^2 = AB^2 - AD^2[/tex]
[tex]BD = \sqrt{AB^2 - AD^2[/tex]
[tex]BD = \sqrt{500^2 - 403.75^2[/tex]
[tex]BD = \sqrt{86985.9375[/tex]
[tex]BD = 294.93[/tex]
