Sides in a right angled triangle

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Presentation transcript:

Sides in a right angled triangle Pythagoras’ result Sides in a right angled triangle

The result: long side H2 = A2 + B2 H A B

The result: long side H2 = A2 + B2 To find the length of the long side: H A B

The result: long side H2 = A2 + B2 To find the length of the long side: H A Find the squares of the two shortest sides, add the result, take the square root of the total… B

Example: long side H2 = A2 + B2 To find the length of the long side: ? 12 cm 8 cm

Example: long side H2 = A2 + B2 To find the length of the long side: ? 12 cm 122 = 144 Square short sides 82 = 64 8 cm

Example: long side H2 = A2 + B2 To find the length of the long side: ? 12 cm 122 = 144 Square short sides 82 = 64 144 + 64 = 208 Add 8 cm

Example: long side H2 = A2 + B2 To find the length of the long side: ? 12 cm 122 = 144 Square short sides 82 = 64 144 + 64 = 208 Add 8 cm √208 = 14.4 Square root

Your turn A. B. ? 10cm ? 10cm 8 cm 100 cm C. D. 13cm 18 cm 5cm ? Is this triangle right angled?

Your turn: Answers A. B. 12.8 10cm 100.5 10cm 8 cm 100 cm C. D. 13cm 19.0 No, but close 14.1 cm 12 cm Is this triangle right angled?

The result: short side A2 = H2 - B2 To find the length of the short side: H A B

The result: short side A2 = H2 - B2 To find the length of the short side: H A Find the squares of the long side and the other short side, find the difference, take the square root of the total… B

Example: short side A2 = H2 - B2 10 cm ? 7 cm

Example: short side A2 = H2 - B2 To find the length of the short side: 10 cm ? 7 cm

Example: short side A2 = H2 - B2 To find the length of the short side: 10 cm ? 102 = 100 Square known sides 72 = 49 7 cm

Example: short side A2 = H2 - B2 To find the length of the short side: 10 cm ? 102 = 100 Square known sides 72 = 49 100 - 49 = 51 Subtract 7 cm

Example: short side A2 = H2 - B2 To find the length of the short side: 10 cm ? 102 = 100 Square known sides 72 = 49 100 - 49 = 51 Subtract 7 cm √51 = 7.14 cm Square root

Your turn A. B. 13cm 8cm 75cm 15cm ? ? C. D. 20cm ? 12cm Diagonal is 14.1 cm long How long is side?

Your turn: answers A. B. 13cm 8cm 75cm 15cm 73.5cm 10.2cm C. D. 20cm Diagonal is 14.1 cm long How long is side?

Mixed problems

Mixed problems Find the right angle

Mixed problems Find the right angle Opposite side is always longest

Mixed problems Find the right angle Opposite side is always longest If you know both short sides: square and add

Mixed problems Find the right angle Opposite side is always longest If you know both short sides: square and add If you know a long and a short side: square and subtract

Mixed problems Find the right angle Opposite side is always longest If you know both short sides: square and add If you know a long and a short side: square and subtract Take square root at the end…

Example A ladder leans against a wall. The ladder is 15ft long, and the foot of the ladder is placed 3 ft away from the wall. How high up the wall does the ladder reach?

Example Right angle is assumed to be between wall and ground!

Example Right angle is assumed to be between wall and ground! The 15ft ladder is the longest side

Example Right angle is assumed to be between wall and ground! The 15ft ladder is the longest side 15ft ? The height up the wall is the missing short side 3ft

Example Right angle is assumed to be between wall and ground! The 15ft ladder is the longest side 15ft ? The height up the wall is the missing short side 152 - 32 = 225 - 9 = 216 3ft

Example Right angle is assumed to be between wall and ground! The 15ft ladder is the longest side 15ft ? The height up the wall is the missing short side 152 - 32 = 225 - 9 = 216 3ft √216 = 14.7 ft

Your turn Find the mixed exercises in your textbook Make sure you know where the right angle is Check that your answers make sense (the longest side must always be less than the sum of the two short sides!)