Question 3 of 18beginner🔧 ApplyNumerical2 marks

Given 15 cot A = 8, find sin A and sec A.

Correct Answer

sin A = 15/17, sec A = 17/8

Exercise: EXERCISE 8.1 | Q: 4 | (Page Page 9)
For More Understanding

Explanation

This question tests the student's understanding of trigonometric ratios in a right triangle and their interrelationships. The student needs to use the definition of cotangent to find the sides of a right triangle, then apply Pythagoras theorem to find the hypotenuse, and finally calculate sin A and sec A using their definitions.

Solution Steps

  1. Step 1: Given 15 cot A = 8, therefore cot A = 8/15.

  2. Step 2: In a right triangle ABC, right-angled at B, cot A = adjacent side/opposite side = AB/BC = 8/15.

  3. Step 3: Let AB = 8k and BC = 15k. By Pythagoras theorem: AC² = AB² + BC² = (8k)² + (15k)² = 64k² + 225k² = 289k². Therefore, AC = 17k.

  4. Step 4: sin A = opposite/hypotenuse = BC/AC = 15k/17k = 15/17.

  5. Step 5: sec A = hypotenuse/adjacent = AC/AB = 17k/8k = 17/8.

PreviousNext