Question

May u please help me with my geometry study guide Only 2 questions

Answer 1

4.

`x=AB=\frac{5\sqrt[]{2}}{2}`

5.

`BC=x=5\sqrt[]{3}`

Explanation:

Relationships in a right triangle:

The sine of an angle is the length of the opposite side to the angle divided by the hypotenuse.

The cosine of an angle is the length of the adjacent side to the angle divided by the hypotenuse

The tangent of an angle is the length of the opposite side to the angle divided by the length of the adjacent side to the angle.

Question 4:

hypotenuse is 5.

AB is adjacent to an angle of 45º. So

`\sin 45^(\circ)=(x)/(5)^{}^{}`
`\frac{\sqrt[]{2}}{2}=(x)/(5)`

Applying cross multiplication:

`2x=5\sqrt[]{2}`
`x=AB=\frac{5\sqrt[]{2}}{2}`

Question 5:

Hypotenuse is 10.

BC is opposite to an angle of 60. So

`\sin 60^(\circ)=(x)/(10)`
`\frac{\sqrt[]{3}}{2}=(x)/(10)`
`2x=10\sqrt[]{3}`
`x=\frac{10\sqrt[]{3}}{2}`
`BC=x=5\sqrt[]{3}`