Question

Can anybody explain this to me

Answer 1

See explanation

Explanation:

Use trigonometric functions definitions:

`\cos \theta =\frac{\text{Adjacent leg}}{\text{Hypotenuse}}\\ \\\sin \theta =\frac{\text{Opposite leg}}{\text{Hypotenuse}}\\ \\\tan \theta =\frac{\text{Opposite leg}}{\text{Adjacent leg}}`

1. Using the definition,

`\sin A=(5)/(13)\\ \\\cos A=(12)/(13)\\ \\\tan A=(5)/(12)\\ \\\sin C=(12)/(13)\\ \\\cos C=(5)/(13)\\ \\\tan C=(12)/(5)`

2. By the Pythagorean theorem,

`WX^2=XY^2+YW^2\\ \\WX^2=12^2+9^2=144+81=225\\ \\WX=15`

Using the definition,

`\sin W=(12)/(15)=(4)/(5)\\ \\\cos W=(9)/(15)=(3)/(5)\\ \\\tan W=(12)/(9)=(4)/(3)\\ \\\sin X=(9)/(15)=(3)/(5)\\ \\\cos X=(12)/(15)=(4)/(5)\\ \\\tan X=(9)/(12)=(3)/(4)`

3. By the Pythagorean theorem,

`ML^2=ME^2+EL^2\\ \\34^2=16^2+ME^2\\ \\ME^2=34^2-16^2=(34-16)(34+16)=18\cdot 50=900\\ \\ME=30`

Using the definition,

`\sin L=(30)/(34)=(15)/(17)\\ \\cos L=(16)/(34)=(8)/(17)\\ \\\tan L=(30)/(16)=(15)/(8)\\ \\\sin M=(16)/(34)=(8)/(17)\\ \\cos M=(30)/(34)=(15)/(17)\\ \\\tan M=(16)/(30)=(8)/(15)`