TRIGONOMETRY (10th Class) Exercise 8.1 Ques 1: In $\triangle ABC$, right angle at B, $AB = 24 \text{ cm}$, $BC = 7 \text{ cm}$. Determined: (i) $\sin A, \cos A$ (ii) $\sin C, \cos C$ Sol: Let us draw a triangle $\triangle ABC$ By using the Pythagoras theorem, we have $AC^2 = AB^2 + BC^2$ (trigonometry, right triangle, Pythagorean theorem, sine, cosine)

Step 1: Calculate the hypotenuse using the Pythagorean theorem

We are given a right-angled triangle $\triangle ABC$ with the right angle at B. We know the lengths of the two sides $AB = 24 \text{ cm}$ and $BC = 7 \text{ cm}$. To find the trigonometric ratios, we first need to find the length of the hypotenuse $AC$ using the Pythagorean theorem.

Step 2: Substitute values and solve for AC

Substitute the given values of $AB = 24 \text{ cm}$ and $BC = 7 \text{ cm}$ into the Pythagorean theorem. Calculate the squares, sum them up, and then take the square root to find the length of the hypotenuse $AC$.

Step 3: Determine $\sin A$ and $\cos A$

For angle $A$, the side opposite to it is $BC$, and the side adjacent to it is $AB$. The hypotenuse is $AC$. We use the definitions of sine (opposite/hypotenuse) and cosine (adjacent/hypotenuse) to find their values.

Step 4: Determine $\sin C$ and $\cos C$

For angle $C$, the side opposite to it is $AB$, and the side adjacent to it is $BC$. The hypotenuse remains $AC$. We again apply the definitions of sine and cosine to find their values for angle $C$.

More from this chapter

• **EXERCISE 8.3** **1.** Express the trigonometric ratios sin A, tan A and sec A in terms of cot A.
• Cos A / 1 + sin a + 1 + sin a / cos A is equal to 2 sec a
• write all the other trigonometric ratios of angle A in terms of sec A
• Express all the trigonometric ratios in terms of Sin A
• Express the trigonometric ratio sign a sec a tan a in terms of cot a
• Prove that √(sec² A + csc² A) = tan A + cot A
• (secθ - tanθ) = (1)/(m) --- (2) Adding (1) & (2) secθ + tanθ + secθ - tanθ = (1)/(m) + (m)/(1) 2secθ = (1 + m²)/(m) secθ = (1 + m²)/(2m) (Hence proved) 2) If as
• If tanθ + secθ = m, prove that secθ = (m² + 1)/(2m).

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