a simple questions about TRIGONOMETRY (obtuse triangles)?

Question

i have 4 question.

(small letter means sides, capital means angle)
1. Triangle PQR.
[p]=18
[Q]=46degree
[R]=39deg.

2. Triangle PQR(again)
[p]=27
[Q]=113degree
[r]=43


3. two roads intersect at an angle of 102.1 degree. Your friend's mailbox is 476 ft. from the intersection. Your mailbox is on the other road and is 615 ft from the intersection. How far is it from your mailbox to your friend's mailbox?.

4. you measure the angle of elevation to an airplane as 46.3 degree. At the same time your friend, who is 600ft closer to a point directly beneath the plane measures the angle of elevation as 47.5 degree. Find the altitude of the plane.

please help me i am a slow learner when it comes to trigo.. i need solutions. please help me!!!.. thanks.

ITS OBLIQUE NOT OBTUSE SORRY...

Answer 1

I don't know what you want finding out for the first two so i will explain how to get the angles and sides. *Note that ?/? is a fraction, ?^? is to the power of.

1.First find the last angle P which is 95 deg.
Next find out side q.
You need to use the sine rule for this so q/Sin 46 = 18/Sin 95
Multiply both sides by Sin 46 to get q=18sin46/sin95
On your calculator work this out to get 13.0 (1decimal place)
The to work out r, you also use the sine rule.
r/sin39= 18/sin95. Multiply both sides by sin 39 to get r = 18sin39/sin 95
This equals 11.4 (1d.p)

2. To find the side q use the cosine rule. Which means that q^2 =27^2+43^2-2*27*43Cos113
This means that q^2=3485.3 (1d.p) Square root that to get q=59.0 (1d.p)
To find angle P you also need to use the cosine rule. So CosP=43^2+59^2-27^2 / 2*43*59
So CosP=0.90677, this means that P=24.9 deg. 1d.p
To find the last angle, R, just take 113 and 24.9 away from 180 to get 42.1 deg.

3. To find the distance between my mailbox and your friends (x), you use the Cosine rule. So x^2=476^2+615^2-2*476*615Cos102.1
x^2=727528.47
x=826.0ft (1d.p)

4. The altitude is the height of an imaginary triangle (h).
First find the angle between the two people (the last angle in the triangle.) This is 86.2 deg.
Then use the Sine rule to find the length between your friend and the plane (y). So y/sin 43.6 = 600/sin86.2. This means that y = 600sin 43.6/sin 86.2. So y= 414.7 (1d.p)
To find h You also need to use the Sine rule, so h/sin47.5= 414.7/sin90
h= 305.7 (1d.p)

Sorry this looks really confusing but I hope it helps.

Answer 2

You want to use the law of sines for solving 1 and 2 and may all the problems.

See http://en.wikipedia.org/wiki/Law_of_sines

For 1) you can calculate the 3rd angle since all angles sum to 180 and you have 2 of them. Then using the law of sines you can compute the length of the other 2 sides.

For 2) you can calculate the 2nd angle using the law of sines, then the 3rd angle from the fact that the sum of the sides is 180. Therefore you can calculate all sides.

Answer 3

Draw a ideal triangle with the ideal proportions. Then use the Pythagorean Theorem to fill in the blanks. word in the diagram, the adjacent section is a million and the hypoteneuse is 3. {cos = A/H} this shall we you calculate the lacking section length of sqrt[8] Sin = O/H = sqrt[8] / 3 OR -sqrt[8]/3 as we can by no skill confirm which quadrant this strategies-set lies in. in case you propose csc^2[A] for the different one, then csc = a million/sin = 3/sqrt[8]. sq. this to get 9/8 be wakeful that the destructive value for sin will grant precisely the same answer as immediately as squared. in case you propose csc[2A], it extremely is a lot harder, yet i think of it extremely is cosecant squared. i wish this helps

Answer 4

180-46-39 = 95
[p]=18
[Q]=46 deg.
[R]= 39 deg.
[P]= 95 deg.