Question

A right triangle has side lengths 5,12, and 13 as shown below.

Answer 1

Answer:
`\sin M=(12)/(13)`

`\cos M=(5)/(13)`

`\tan M=(12)/(5)`

Explanation:

According to trigonometry , For any angle x in a right triangle we have

`\sin x=\frac{\text{Side opposite to x}}{\text{Hypotenuse}}`

`\cos x=\frac{\text{Side adjacent to x}}{\text{Hypotenuse}}`

`\tan x=\frac{\text{Side opposite to x}}{\text{Side adjacent to x}}`

In the given picture , we have ΔMNL right -angled at N with side length 5 , 12 and 13.

∴ Side ML is hypotenuse [∵Side opposite to right angle is the hypotenuse]

i.e. Hypotenuse = 13

Now, For angle M

Side opposite to ∠M = NL = 12

Side adjacent to ∠M = MN= 5

Then,

`\sin M=(12)/(13)`

`\cos M=(5)/(13)`

`\tan M=(12)/(5)`

Answer 2

sin of an angle is opposite leg divided by hypotenuse.

sin M = 12 / 13

tan of an angle is opposite leg divided by adjacent leg

tan M = 12 / 5

cos of an angle is adjacent leg divided by hypotenuse

cos M = 5 / 13