In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
AT = 10
∠ ADT = 45°
Step 02:
right triangle (isosceles triangle):
we must analyze the figure to find the solution.
AT = opposite
AD = adjacent
TD = hypotenuse
sin α = opposite / hypotenuse
[tex]\begin{gathered} \sin \text{ 45 = }\frac{10}{TD} \\ \\ TD\cdot\text{ sin 45 = 10} \\ \\ TD\text{ = }\frac{10}{\sin \text{ 45}}\text{ = }14.14 \end{gathered}[/tex]
cos α = adjacent / hypotenuse
[tex]\begin{gathered} \cos \text{ 45 = }\frac{AD}{14.14} \\ \\ 14.14\cdot\cos \text{ 45 = AD} \\ \\ 10\text{ = AD} \end{gathered}[/tex]
∠ TAD = 90°
∠ ATD = (180 - 90 - 45)° = 45°
The answer is:
∠ ADT = 45°
∠ TAD = 90°
∠ ATD = 45°
AT = 10
TD = 14.14
AD = 10
