SSC CHSL Tier 1 2017 Quantitative Aptitude Questions with Solutions

Explanation

In a right-angled triangle ABC, the sum of all interior angles is 180°. Since the triangle is right-angled at B, we have ∠B = 90°. Given that ∠C = 60°, the measure of ∠A is:

∠A = 180° - 90° - 60° = 30°

Using the standard trigonometric values, the value of cot 30° is √3. Substituting ∠A = 30° into the required expression:

cot A - ½ = √3 - ½ = (2√3 - 1) / 2

Explanation

In a right-angled triangle ABC with angle B = 90°, the trigonometric ratio cosec A is defined as the ratio of the hypotenuse to the opposite side.

cosec A = AC / BC = 13 / 12

Let AC = 13k and BC = 12k, where k is a positive constant.

By applying the Pythagorean theorem, the adjacent side AB can be expressed as:

AB = √(AC² - BC²)

AB = √((13k)² - (12k)²)

AB = √(169k² - 144k²)

AB = √(25k²) = 5k

Given that the length of side AB is 10 cm:

5k = 10

k = 2

Therefore, the length of side AC is:

AC = 13k = 13 × 2 = 26 cm