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?

Question

asked Dec 2, 2023 65.8k views

1 Answer

Rody · Answer 1 · 2023-12-06T04:06:27+0000

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:

$\angle A\approx31.5$