maths? trigonometry?

Question

Town A is 155km south of town B. Town C is 218km west of town B. Find the bearing and the distance of town C from town A.

b. A kite string is pinned to the ground. The string makes an angle of 53o43' to the ground and is 80m long. How high is the kite above ground level.

a. The shadow of a tree is 40 in length and the angle of elevation from the end of the shadow to the top of the tree is 34o14'. Find the height of the tree to the nearest 1/10 of a metre

c. Find the measure of all angles of a triangle with sides 3cm, 4cm and 5cm

Answer 1

Towns - use pythagoras and tangent.
Kite - use sine
Tree - use tangent with complementary angle.
Triangle - 3,4,5 is right angled so sine, cosine or tangent for other angles.

Answer 2

a. Just draw the triangle as you desrcibe it.

C ---218------B

155

A

They want the bearing c FROM a... so if you look at it in your drawing its an obtuse angle, so we just work out the theta inside the triangle, and then do 360-theta.

So we have opposite and adjcent so its tan

so

tan(theta) = 218/155
theta = 54 deg 35 min (rounded to nearest min)

so bearing is

365 - 54 deg 35 min = 310 deg 25 min

b. Same goes for all these questions, just draw in the diagram and see what ratio you get. For the kite you have the angle of elevation, and the hypotenuse and it wants the opposite.. so you have sin(53 deg 43') = O / 80

so = 80 * sin(53 deg 43') (the answer will be in meters)

a. shadow of a tree question is almost same as kite q so draw the diagram, put the vals in and work it out

c. that is an easy question, just draw the triangle (the 5cm will be the hyp) and do sin(theta) = O/H etc... you will need to use inverse sin button...

Hope that helps

Laura

Answer 3

till now you utilize any computing help please memorise a suitable perspective triangle and its 2 angles (that are lass than ninety tiers) you will possibly be able to evaluate 'any a sort of two angles' as perspective alpha. an ingredient opposite to perspective alpha is opposite part (O) an ingredient adjoining to perspective alpha is adjoining part (A) A Hypotenuse is often opposite to ninety degree perspective (H) Memorise as O/H = sine alpha-----> and H/O = Co secant A/H = Cos alpha------> and H/A= Secant O/A= Tan alpha---> and A/O = Co-tangent that's bare minimum necessary expertise till now making use of a calculator! undergo in recommendations there are inverse purposes for all relatives mentioned above although calculator exhibits all trigonometric purposes on it consumer reminiscence is important to effectively use it! shop that reminiscence straightforward and usable continuously! ultimate merchandise of trigonometry is to prepare relatives of suitable angled triangles (relatives of angles and aspects) Technically trigonometry makes use of the two angles and co-ordinates of triangle vertexes and mentioned relatives grow to be complicated as quickly as we use sin^2 alpha, or sin^3 alpha or any larger order! you will possibly be able to construct a means to stay away from complicated computing via not getting to understand complicated relatives! Regards!

Answer 4

Phthagorean Theorem

C² = a² + b²

√c² = √(155)² + (218)²

√c² = √24025 + 47524

√c² = √71549

c = 267.4864483 km

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sinθ = y / r

sin53.7166666666 = y / 80

80(0.806100458) = 80(y/80)

80(0.806100458) = y

64.48803662 m

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tanθ = y / x

tan 34° 14' = y / 40

tan 34.2.33333333 = y / 40

40(0.680450108) = 40(y/40)

40(0.680450108 = y

27.2180043 = y

27.2 inches = y

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