Question

3) In triangle ABC, right angled at B,
AC = 13 cm , AB = 5 cm then sin A =​

Answer 1

Step-by-step explanation:

Angle ABC is a right angle at B. If AC=5cm and BC=13cm, what is the length of AB?

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Angle ABC is a right angle at B. If AC=5cm and BC=13cm, what is the length of AB?

With what you stated the hypotenuse, which is always opposite the right angle, would be side AC. But the hypotenuse is always the longest side, but 5 < 13.

Is this what you actually have in mind?

Because with what you stated the hypotenuse, which is always opposite the right angle, would be side AC. But the hypotenuse is always the longest side, but 5 < 13. If so the right angle is at A instead of B. Now you can use the pythagorean theorem.

5^2 + x^2 = 13^2

25 + x^2 = 169 : Subtract 25 on both sides.

x^2 = 144 : Take t

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ABC is a triangle. Angle B is a right angle, making triangle ABC a right triangle. Since angle B is a right angle, the side opposite it, AC, is the hypotenuse, the longest side of any right triangle. You state that AC = 5cm and BC = 13cm, so AC < BC, but since AC is the hypotenuse, it must be greater than either of the other two sides of the triangle. This is a contradiction of the properties of a right triangle. AC must be bigger than both BC and AB, or angle B is not a right angle.

Answer 2

The answer is 12/13

Given,

∠B = 90⁰

AC = 13cm

AB = 5cm

To Find,

sin A

Solution,

Apply Pythagoras theorem,

AC² = AB² + BC²

(13)² = (5)² + BC²

169 = 25 + BC²

∴ BC² = 169 - 25

∴ BC = √144

⇒ BC = 12cm

Sin A = Opposite/Hypotenuse

Sin A = BC/AC

∴ Sin A = 12/13

Hence, the answer is 12/13.