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#1 2007-08-16 03:17:26

Rocking_math
Guest

Just some help with Trig!

A few questions that I don't get mad!


Q1 Sam and Markus are standing on level ground 100 metres apart. A large tree is due North of Markus and on a bearing of 065o from Sam. The top of the tree appears at an angle of elevation of 25o to Sam and 15o to Markus. Find the height of the tree.

Q2 A rally car drives at 140kmph for 45 minutes on a bearing of 032o and then 180 kmph for 40minutes on a bearing 317o. Find the distance and bearing of the car form its starting point.

Just these two....

Thanks big_smile

#2 2007-08-16 04:14:26

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Just some help with Trig!

Q1

Let m be the distance between Markus and the tree and s be the distance between Sam and the tree. Then applying the cosine rule to the triangle formed by Markus, Sam and the tree gives

If h is the height of the tree, then

Now solve for m or s from the simultaneous equations and find h.

The answer I got was

≈ 29.16 metres. faint

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#3 2007-08-16 04:41:22

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Just some help with Trig!

Q2

On the first part of the journey, the distance travelled is 140 × 45⁄60 = 105 km. On the second part, the driver drives 180 × 40⁄60 = 120 km. The angle between the two paths is 180° − 32° − (360° − 317°) = 105°. So if d is the distance from the starting point, the cosine rule gives

(I got d ≈ 137.49 km.)

If θ is the angle between the direction of the line joining the final and starting points and the direction the car travels on the first part of its journey, the sine rule gives

θ turns out to be greater than 32°, so the final bearing of the car is given by 360° − (θ − 32°) (≈ 334.53° by my calculation).

Last edited by JaneFairfax (2007-08-16 07:09:57)

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#4 2007-08-16 09:42:04

Rocking_math
Guest

Re: Just some help with Trig!

Thanks man!

I could never get these bearing questions swear!!

#5 2007-08-16 10:29:56

mikau
Member
Registered: 2005-08-22
Posts: 1,504

Re: Just some help with Trig!

hehe, Jane is no man.


A logarithm is just a misspelled algorithm.

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