Identify the trigonometric values for angles A and B in the given right-angled triangle.

Summary:

Step-by-step solution:

The image displays a right-angled triangle. Let's assume the vertices are A, B, and C, with the right angle at C. The side opposite angle A is BC, the side opposite angle B is AC, and the hypotenuse is AB.

From the image, we can identify the following:

• Side AC = 5
• Hypotenuse AB = 13
• Angle C is the right angle (90 degrees).
• Side BC is unknown, let's denote it as 'x'.

First, we can find the length of side BC using the Pythagorean theorem: $$ $$AC^2 + BC^2 = AB^2$$ $$.

$$ $$5^2 + x^2 = 13^2$$ $$

$$ $$25 + x^2 = 169$$ $$

$$ $$x^2 = 169 - 25$$ $$

$$ $$x^2 = 144$$ $$

$$ $$x = √{144}$$ $$

$$ $$x = 12$$ $$. So, BC = 12.

Now, we can calculate the trigonometric values:

For angle A:

• Cosine (cos A): Adjacent side / Hypotenuse = AC / AB = 5 / 13
• Sine (sin A): Opposite side / Hypotenuse = BC / AB = 12 / 13
• Tangent (tan A): Opposite side / Adjacent side = BC / AC = 12 / 5
• Cotangent (cot A): Adjacent side / Opposite side = AC / BC = 5 / 12

For angle B:

• Cosine (cos B): Adjacent side / Hypotenuse = BC / AB = 12 / 13
• Sine (sin B): Opposite side / Hypotenuse = AC / AB = 5 / 13
• Tangent (tan B): Opposite side / Adjacent side = AC / BC = 5 / 12
• Cotangent (cot B): Adjacent side / Opposite side = BC / AC = 12 / 5

Final Answer:

cos A = 5/13

sin A = 12/13

tg A = 12/5

ctg A = 5/12

cos B = 12/13

sin B = 5/13

tg B = 5/12

ctg B = 12/5