Right Angled Trigonometry 05 January 2022 Pythagoras Theorem

Pythagoras Theorem Hypotenuse c a b NB To find the Hypotenuse we must square

Example Find the length of PQ correct to 2 significant figures Q 15 m

Example Find the value of y correct to 1 decimal place. y 3. 7

Example A ladder 17 m long reaches 15 m up a vertical wall. If

Example Calculate the length of PQ in the triangle PQR Opp Hyp Adj

Example Calculate the length XY in the triangle XYZ Hyp Opp Adj

Example Calculate the length of BC in the triangle ABC. Hyp Opp 12 Adj

Example A surveyor, P, is 1000 m away on horizontal ground from the foot

Example From the top of a vertical cliff 100 m high the angle of

Example Calculate the size of angle A in the triangle ABC Opp Adj Hyp

Example (i) (ii) Find the size of angle x in each of the following

Example Calculate the size of angle PQR in the triangle below. P 8 →

Example The figure is a pyramid on a square base ABCD. The edges of

a) the length of AC Using pythagoras theorem with the base 42 cm D

5. In triangle DEF, Angle F = 90 , Angle D = 21 and

6. For the diagram drawn below find the lengths of x and y 15

8. Find the height of these stairs correct to one decimal place h 35

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Right Angled Trigonometry 05 January 2022

Pythagoras Theorem Hypotenuse c a b NB To find the Hypotenuse we must square the other sides and then add together. To find any other side we square the sides and subtract. The side is then found by taking the square root.

Example Find the length of PQ correct to 2 significant figures Q 15 m P 21 m R

Example Find the value of y correct to 1 decimal place. y 3. 7 cm 14. 3 cm

Example A ladder 17 m long reaches 15 m up a vertical wall. If it rests on horizontal ground, how far is its foot from the foot of the wall? 17 m 15 m

Formulae to learn c Hyp a Opp Adj b A

C b a B c A

Trig Ratios for 45° 1 1 45 1

Trig ratios for 30° and 60° 30 2 60 1

Example Calculate the length of PQ in the triangle PQR Opp Hyp Adj

Example Calculate the length XY in the triangle XYZ Hyp Opp Adj

Example Calculate the length of BC in the triangle ABC. Hyp Opp 12 Adj

Example A surveyor, P, is 1000 m away on horizontal ground from the foot of a radio mast, QR. From P the angle of elevation of the top, R, of the mast is 20. Find the height of the mast. Assume the surveyor’s height to be negligible. R With a written problem the first step is to draw a sketch. Hyp opp S 20 1000 Adj P

Example From the top of a vertical cliff 100 m high the angle of depression of a boat out at sea is 32. How far is the boat from the foot of the cliff? 32 100 Opp Hyp 32 Adj d

Example Calculate the size of angle A in the triangle ABC Opp Adj Hyp

Example (i) (ii) Find the size of angle x in each of the following

(iii)

Example Calculate the size of angle PQR in the triangle below. P 8 → Q 3

Example The figure is a pyramid on a square base ABCD. The edges of the base are 30 cm long and the height, EH, of the pyramid is 42 cm. Find a) the length of AC b) the angle EAH

a) the length of AC Using pythagoras theorem with the base 42 cm D A 30 cm B b) the angle EAH 30 cm E Draw the right angled triangle for EAH 42 cm A H 21. 21 cm C