FTE Maths help please...

[AdamLT]

Hi all

I hope it's ok posting this sort of question in this forum. There are just 2 q's I am a little unsure of from the FTE test guidance notes, and wondered if someone could assist me in the working out of them.

Q1. In any triangle, using the normal convention for sides and angles:

a2 = b2 + c2 – 2 x b x c x cosA

(note; it is normal, in mathematical equations, to write 2 x b x c x cosA as 2bccosA and this convention will be used in the formulae in the rest of these questions)

The formula would now be written as follows:

a2 = b2 + c2 – 2bccosA

Using this formula, find the value of A in the triangle below.




A
6cm / \ 7cm
/ \
C ----- B
9cm

(cant get the triangle to stay drawn properly. its a scalene triangle, A (top) to B (bottom right) is 7cm, B to C (bottom left) is 9cm and C to A is 6cm)

Q2. The formula tanq = V2/gr relates the radius of turn (r metres) of an aircraft at an angle of bank of qº if it is flying at a speed of V ms-1.

If 1 knot = 0.514 ms-1, find the radius of turn, in metres, of an aircraft at an angle of bank of 45º flying at a speed of 300 knots.

I'd appreciate any help you can offer

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[pilotmike]

Re-arrange the formula to:

Angle A = ArcCos((b^2+c^2-a^2)/2bc)
=> Angle A = ArcCos((49+36-81)/84)
=> Angle A = ArcCos(1/21)
=> Angle A = 87.3 degrees


For radius of turn, re-arrange the formula to:
r = v^2/g
=> r = ((300 * 0.514)^2) / 9.81 = 2423.8, being 2.4238 km or about 1.5 miles or about 1.3 NM

Hope this helps

PM

[AdamLT]

cheers for the assisstance guys. much appreciated

[Bigga]

1) 87.27
2) 2423.82
is what i got, btw you are allowed to use a calculator right??

[AdamLT]

Bigga

yes you are. i was just unsure how you did these sort of q's. i'ts been 10 years since i did my GCSE maths..so just brushing up on these sorts of q's. i had the answers, but wanted to know how to do them

thanks

[AdamLT]

bobby_101

they are practice questions forarded by FTE in preparation for their tests.