Question

In triangle ANO, angle P measures 90°, PN = 34 feet, and OP = 40 feet. What is the measure of angle A to the nearest degree?

A) 38°
B) 52°
C) 56°
D) 72°

Answer 1

The answer of the given equation that "the measure of angle A to the nearest degree" is C) 56°

Step-by-step explanation:

In a right-angled triangle, the sum of the angles is 180°. Given that angle P measures 90°, the sum of angles A, N, and O is 90°.

`\[ A + N + O = 180° \]`

Substitute the known value:

`\[ A + 90° + O = 180° \]`

Solve for angle A:

`\[ A = 180° - 90° - O \]`

Now, in a right-angled triangle, the sides opposite the angles have a specific relationship. Using the Pythagorean theorem:

`\[ ON^2 + NP^2 = OP^2 \]`

Substitute the given values:

`\[ ON^2 + 34^2 = 40^2 \]`

Solve for ON:

`\[ ON = √(40^2 - 34^2) \]`

Once you find ON, you can use trigonometric ratios to find the value of O.

`\[ \tan(O) = (ON)/(NP) \]`

Now, you can substitute the values into the equation and solve for angle O.

After finding O, substitute it back into the first equation to find angle A.

The final result is approximately 56°, so the correct answer is C) 56°.