Question

1a) Use the pythagorean theorem tofind the missing side length.

1b) write the sin, cosine and tangent of each angle leave answers in fractions. rationalize the denominator if needed.​

Answer 1

Answer with step-by-step explanation:

1a) We are given a right angles triangle and we are to find the missing side length using the Pythagoras Theorem.

`x =\sqrt {(6)^2+(8)^2}`

`x=\sqrt {100}`

`x = 10`

1b) Writing the sine, cosine and tangent for angles a and b:

sin a
`=\frac {8} {10}`

cos a
`=\frac {6} {10}`

tan a
`=\frac {8}{6}`

sin b
`=(6)/(10)`

cos b
`=(8)/(10)`

tan b
`=(6)/(8)`

Answer 2

1)

a)

We are given one leg of triangle as 6 km and the other leg is of length of 8 km.

Hence, the hypotenuse is calculated using Pythagorean theorem as:

`x^2=8^2+6^2\\\\\\x^2=64+36\\\\x^2=100\\\\x=10`

Hence, the hypotenuse of the triangle or the missing side x=10 cm.

Now we calculate trignometric ratio with respect to angle a and b as:

b)

We know that:

Sine of an angle is ratio of perpendicular to hypotenuse.

Cosine of an angle is ratio of base and hypotenuse.

And tangent of an angle is ratio of perpendicular and base.

Angle a:

We have perpendicular=8

Base=6

Hypotenuse=10

Hence,

sin a=8/10

cos a=6/10

tan a=8/6

Angle b:

Perpendicular =6

Base=8

Hypotenuse=10

Hence,

sin b=6/10

cos b=8/10

tan b=6/8