Question

suppose a=2 and A= 70 degrees. find :b=c=B=__ degreesgive all answers to at least one decimal place. give angles in degrees.

Answer 1

Trigonometric Ratios in a Right Triangle

Right triangles are identified because they have an interior angle of 90° (right angle).

In right triangles, the trigonometric ratios are satisfied. For example, the following ratios are defined as:

`\sin \theta=\frac{opposite\text{ leg}}{\text{hypotenuse}}`
`\tan \theta=\frac{\text{opposite leg}}{adjacent\text{ leg}}`

Where the hypotenuse is the side opposite to the right angle.

If we use the angle A=70°:

`\tan A=(a)/(b)`

Solving for b:

`b=(a)/(\tan 70^0)=(2)/(2.7475)=0.7279`
`\sin 70^o=(a)/(c)`

Solving for c:

`c=(a)/(\sin 70^o)=(2)/(0.9397)=2.1284`

Rounding to one decimal place:

b=0.7

c=2.1