TRIGONOMETRY (10th Class)
Exercise 8.1
Ques 1: In △ABC, right angle at B, AB=24 cm, BC=7 cm.
Determined:
(i) sinA,cosA
(ii) sinC,cosC
Sol: Let us draw a triangle △ABC
By using the Pythagoras theorem,
we have
AC2=AB2+BC2
(trigonometry, right triangle, Pythagorean theorem, sine, cosine)
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Step-by-Step Solution
Step 1: Calculate the hypotenuse using the Pythagorean theorem
We are given a right-angled triangle △ABC with the right angle at B. We know the lengths of the two sides AB=24 cm and BC=7 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 cm and BC=7 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 sinA and cosA
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 sinC and cosC
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.