Based on the trigonometry ratios and the Pythagorean theorem both of them were incorrect.
Cos A = 4/5; Sin A = 3/5
<h3>What is the Trigonometry Ratios?</h3>
The Trigonometry ratios relates the length of the sides of a right triangles. They are given as:
- Sine ratio, sin ∅ = opp/hyp
- Cosine ratio, cos ∅ = adj/hyp
- Tangent ratio, tan ∅ = opp/adj.
<h3>What is the Pythagroean Theorem?</h3>
If two sides of a right triangle are known the third side can be determined using the Pythagorean theorem, which is given as, c² = a² + b², where and b are legs, and c is the hypotenuse of the right triangle.
1. Given that tan A = 3/4, it is not necessarily true that BC MUST have a length of 3 units, and AC MUST have a length of 4 units, because:
If BC = 9 units and AC = 12 units, the it will give us the same tangent ratio as:
tan A = 9/12 = 3/4.
Therefore, Angelica's mistake is stating that BC MUST be 3 units, and AC MUST be 4 units.
2. Knowing two length of the sides of a right triangle is enough information needed to find the length of the third side using the Pythagorean theorem, so Graceilla is incorrect.
3. Find AC using the Pythagorean theorem:
AB = √(3² + 4²)
AB = 5 units.
Cos A = adj/hyp = AC/AB
Cos A = 4/5
Sin A = opp/hyp = BC/AB
Sin A = 3/5
Learn more about the trigonometry ratios on:
brainly.com/question/10417664
