Question

Find all missing side and lengths and angle measures of each triangle.

Answer 1

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

`\begin{gathered} \sin \text{ 45 = }(10)/(TD) \\ \\ TD\cdot\text{ sin 45 = 10} \\ \\ TD\text{ = }\frac{10}{\sin \text{ 45}}\text{ = }14.14 \end{gathered}`

cos α = adjacent / hypotenuse

`\begin{gathered} \cos \text{ 45 = }(AD)/(14.14) \\ \\ 14.14\cdot\cos \text{ 45 = AD} \\ \\ 10\text{ = AD} \end{gathered}`

∠ TAD = 90°

∠ ATD = (180 - 90 - 45)° = 45°

The answer is:

∠ ADT = 45°

∠ TAD = 90°

∠ ATD = 45°

AT = 10

TD = 14.14

AD = 10