Question

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Answer 1

$\cos\theta=\frac{\text{5}}{\text{13}}, \ \sin\theta=\frac{\text{12}}{13}, \ \tan\theta=\frac{\text{12}}{\text{5}}$

$\sec\theta=\frac{\text{13}}{\text{5}},\ \csc \theta=\frac{\text{13}}{\text{12}} , \ \cot \theta=\frac{\text{5}}{\text{12}}$

Solution:

Given triangle is a right triangle.

Base = 5, Hypotenuse = 13, Height = ?

Height (h) = opposite

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

$5^2+h^2=13^2$

$25+h^2=169$

$h^2=144$

Taking square root on both sides.

h = 12

$\cos\theta=\frac{\text{Base}}{\text{Hypotenuse}}$

$\cos\theta=\frac{\text{5}}{\text{13}}$

$\sin\theta=\frac{\text{Opposite}}{\text{Hypotenuse}}$

$\sin\theta=\frac{\text{12}}{13}$

$\tan\theta=\frac{\text{Opposite}}{\text{Base}}$

$\tan\theta=\frac{\text{12}}{\text{5}}$

$\sec\theta=\frac{\text{Hypotenuse}}{\text{Base }}$

$\sec\theta=\frac{\text{13}}{\text{5}}$

$\csc \theta=\frac{\text{Hypotenuse}}{\text{Opposite }}$

$\csc \theta=\frac{\text{13}}{\text{12}}$

$\cot \theta=\frac{\text{Base }}{\text{Opposite}}$

$\cot \theta=\frac{\text{5}}{\text{12}}$