0

Guest

Courses New

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

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

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 60787 Points
2 years ago
Let us assume a right angled triangle ABC, right angled at B Given: 15 cot A = 8 So, Cot A = 8/15 We know that, cot function is the equal to the ratio of length of the adjacent side to the opposite side. Therefore, cot A = Adjacent side/Opposite side = AB/BC = 8/15 Let AB be 8k and BC will be 15k Where, k is a positive real number. According to the Pythagoras theorem, the squares of the hypotenuse side is equal to the sum of the squares of the other two sides of a right angle triangle and we get, AC2=AB2 + BC2 Substitute the value of AB and BC AC2= (8k)2 + (15k)2 AC2= 64k2 + 225k2 AC2= 289k2 Therefore, AC = 17k Now, we have to find the value of sin A and sec A We know that, Sin (A) = Opposite side /Hypotenuse Substitute the value of BC and AC and cancel the constant k in both numerator and denominator, we get Sin A = BC/AC = 15k/17k = 15/17 Therefore, sin A = 15/17 Since secant or sec function is the reciprocal of the cos function which is equal to the ratio of the length of the hypotenuse side to the adjacent side. Sec (A) = Hypotenuse/Adjacent side Substitute the Value of BC and AB and cancel the constant k in both numerator and denominator, we get, AC/AB = 17k/8k = 17/8 Therefore sec (A) = 17/8

Think You Can Provide A Better Answer ?

Other Related Questions on 10 grade maths

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More