Question

Use the inverse trigonometric keys on a calculator to find the measure of angle A

Answer 1

49°

Explanation:

49^2 - 32^2 = BC^2

2401 - 1024 = 1377

√1377 = 37.1079506

37.1 m

Sin(A) / 37.1 = Sin(90)/ 49

Sin (A) = 37.1 X Sin(90)/49

A = sin^-1(3.71 X sin90)/49

A = 49.21

Answer 2

The measure of angle A. is approximately
`\( 56.31^\circ \)` when rounded to two decimal places.

In a right-angled triangle ABC where angle ABC is 90 degrees, and sides AC and AB are given as 32 m and 49 m, respectively, we can use trigonometry to find the measure of angle A.

The tangent of an angle in a right-angled triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

`\[ \tan(A) = \frac{{\text{opposite side}}}{{\text{adjacent side}}} \]`

In this case,
`\(\tan(A) = \frac{{AB}}{{AC}}\).`

Using the inverse tangent function
`(\(\tan^(-1)\))` on a calculator, we find:

`\[ A = \tan^(-1)\left(\frac{{49}}{{32}}\right) \]`

Let's calculate
`\( A = \tan^(-1)\left(\frac{{49}}{{32}}\right) \):`

`\[ A = \tan^(-1)\left(\frac{{49}}{{32}}\right) \]`

Using a calculator:

`\[ A \approx \tan^(-1)\left(1.53125\right) \]`

`\[ A \approx 56.31^\circ \]`

Therefore, measure of angle A. is approximately
`\( 56.31^\circ \)` when rounded to two decimal places.

The probable question may be:

In triangle ABC, angle ABC=90 degree, AC=32 m, AB=49 m

Use the inverse trigonometric keys on a calculator to find the measure of angle A. A=_____° (Round the answer to the nearest whole number.)