Question

7. In right triangle ABC shown below, AB = 18.3 and BC = 11.2. С 11.2 A B. 18.3 What is the measure of ZA, to the nearest tenth of a degree?

Answer 1

On a right triangle, the tangent of an angle equals the length of the side opposite to it over the length of the side adjacent to it. Then:

`\tan (\angle A)=(BC)/(BA)`

Substitute the values for BC and BA:

`\tan (\angle A)=(11.2)/(18.3)`

Take the inverse tangent function to both sides of the equation to isolate the angle A:

`\angle A=\tan ^(-1)((11.2)/(18.3))`

Use a calculator to evaluate the expression on the right hand side of the equation:

`\angle A=31.46754337\ldots`

Then, to the nearest tenth:

`\angle A\approx31.5`