Question

In right triangle LMN, L and M are complementary angles and sin(L) is 19/20. What is cos(M).

Answer 1

Option A:

$\cos M=\frac{19}{20}$

Solution:

The image of the triangle is attached below.

Given data:

$\sin L=\frac{19}{20}$

Using trigonometric ratio formulas,

$\sin L=\frac{\text { Opposite side of } L}{\text { Hypotenuse }}$

$\sin L=\frac{MN}{LM}$

So, MN = 19 and LM = 20

Using Pythagoras theorem,

In right triangle, square of the hypotenuse is equal to the sum of the squares of the other two sides.

$LM^2=LN^2+MN^2$

$20^2=LN^2+19^2$

$400=LN^2+361$

Subtract 361 from both sides,

39 = LN²

Taking square root on both sides,

$LN=\sqrt{39}$

$\cos \theta=\frac{\text { Adjacent side of } \theta}{\text { Hypotenuse }}$

$\cos M=\frac{\text { Adjacent side of } M}{\text { Hypotenuse }}$

$\cos M=\frac{MN}{LM}$

$\cos M=\frac{19}{20}$

Hence option A is the correct answer.