Question

Here is a triangle. Find cos(A), sin(A), and tan(A). Explain your reasoning.

Answer 1

`\cos(A)=(3√(10))/(10)`

`\sin(A)=(√(10))/(10)`

`\tan(A)=\frac13`

Explanation:

Calculate the hypotenuse of ΔABC using Pythagoras' Theorem:
`a^2+b^2=c^2` (where a and b are the legs and c is the hypotenuse of a right triangle)

Given:

• a = 2
• b = 6

`\implies 2^2+6^2=c^2\\\\\implies 4 + 36 = c^2\\\\\implies c^2=40\\\\\implies c=√(40) \\\\\implies c=2√(10)`

Trig ratios:

`\sin(\theta)=(O)/(H) \ \ \ \ \cos(\theta)=(A)/(H) \ \ \ \ \tan(\theta)=(O)/(A)`

where
`\theta` is the angle, O is the side opposite the angle, A is the side adjacent the angle, H is the hypotenuse in a right triangle.

`\cos(A)=(6)/(2√(10) )=(3√(10))/(10)`

`\sin(A)=(2)/(2√(10) )=(√(10))/(10)`

`\tan(A)=(2)/(6)=\frac13`