Question

Can someone help me with 7 , 8 and 9 please

Answer 1

Since all of the triangles in question are right triangles, we can use the following formulas:

`\sin \theta=(os)/(h)`
`\cos \theta=(as)/(h)`
`\tan \theta=(os)/(as)`

Where os is the side opposite to the angle θ, as is the side adjacent to the angle and h is the triangle's hypotenuse.

Now we must consider which formula to use on each of the trianles in question to get the asked quantity.

On 7, we are given an angle, its adjacent side and are asked to find the opposite side, thus we should consider using the formula for the tangent. That is

`\tan (55)=(x)/(5)`

`1.43=(x)/(5)`
`x=7.15`

For 8, once again we are given an agle, its adjacent side and are asked to find its opposite side, so we'll do the same.

`\tan (37)=(x)/(3)`
`0.75=(x)/(3)`
`x=2.25`

And finally for 9 we are given an angle, its opposite side and are asked to find its adjacent side, so even though it is slighlty different, we can solve it the same as before:

`\tan (62)=(12)/(x)`
`x\cdot\tan (62)=12`

`x=(12)/(\tan (62))`
`x=(12)/(1.88)`
`x=6.38`

Thus, the sides we were tasked with finding for triangles 7, 8 and 9 are, respectively, 7.15, 2.25 and 6.38.