Question

Help w/ Trig Questions? #3

Hi, here are just the final two questions. I know you like to answer them as separate but there are way too many. Please show your work and make a picture to help!

Answer 1

Q.No.9 `-` `AB=275.35` `m` and area of triangle is `2.8523` hectares

Q.No.7 `-` `AG` makes the angle `33.9^@` with the plane.

Explanation:

Q.No.9 `-` We can use sine formula for a triangle as in a `DeltaABC`, we have

`(BC)/sinA=(AC)/sinB=(AB)/sinC`

• note that `m/_A=180^@-54^@-67^@=59^@`

Hence `(BC)/(sin59^@)=242/(sin54^@)=(AB)/(sin67^@)`

or `(BC)/0.8572=242/0.8090=(AB)/0.9205`

Hence `AB=0.9205xx242/0.8090=275.35`

note that we use `a` for `BC`, `b` for `AC` and `c` for `AB`

Area of triangle is given by

`1/2xxbcxxsinA=1/2xx242xx275.35xx0.8572=28523.33` `m^2`

or `28523.33/10000=2.852333` or say `2.8523` hectares

Q.No.7 `-` `AG` makes the angle `AGE` with the plane `EFGH`. Observe that it is a right angle, whose altitude `AE=6` `cm.`

and `EG` can be worked out as it is hypotenuse of right angled triangle `EGH`. As `EH=4` `cm.` and `HG=8` `cm.`,

`EG=sqrt(4^2+8^2)=sqrt(16+64)=sqrt80=8.9443`

Hence `tan/_AGE=6/8.9443=0.67082` and from tables fot tangent ratio we get

`m/_AGE=33.9^@`

Answer 2

Question 9

`/_BAC=180^@-67^@-54^@=59^@`

By sine rule for `Delta ABC`

`(AB)/sinC=(AC)/sinB=(BC)/sinA`

Length of the fence AB
`=>AB=(AC)/sinBxxsinC=242/sin54xxsin67=275.3m`

Again

Length of the fence BC
`=> BC =(AC)/sinBxxsinA=242/sin54xxsin59=256.4m`

Area of `Delta ABC=1/2xxACxxBCxxsinC`

`=1/2xx242xx275.3xxsin67 m^2~~30663m^2=3.0663" hectares"`